# Exponential Growth and Decay

### Topic Page

Exponential Growth and Decay### Questions

- How do I find an exponential growth function in terms of #t#?
- What is exponential growth?
- How do I find the multiplier for a rate of exponential decay?
- How is exponential decay related to a half-life?
- How to find an equation of exponential decay?
- What happens when something grows exponentially?
- How long does it take the culture to double its mass if a bacterial culture which is growing exponentially increases from 5 g to 7 g in 11 hours?
- Joe Smith invest his inheritance of $50,000 in an account paying 6.5% interest. If interest is compounded continuously, how long will it take for the account to be $200,000?
- How do you write an exponential equation that passes through (1, 1.5), (-1, 6)?
- How do you write an exponential equation that passes through (0,3) and (2,6)?
- How do you write an exponential equation that passes through (-1, .5) and (2, 10)?
- How do you write an exponential equation that passes through (0, -2) and (2, -50)?
- Is #y = -3^x# an exponential function?
- Question #70b92
- A certain species of fish has been declining in population by 7% per year. That means its rate of decay is 0.93. What is the fish population in year 4 if the initial population was 500,000?
- What is the balance if $20,000 is invested at an annual rate of 7.8 percent for 5 years, compounded continuously. How long will it take for the original amount to double in size?
- Question #44bee
- With 300 being the y intercepts and an additional point being (3,450) How do you find a formula in the format of #ab^x#?
- How do you find the exponential function f(x)= a^x whose graph goes through the point (3, 1/125)?
- A bacteria culture initially contains 1500 bacteria and doubles every half hour. The formula for the population is p(t)= 1500e^kt for some constant k, how do you find the size of the population after 60 minutes?
- How do you determine the formula for the graph of an exponential function given (0,3) and (2,6)?
- How do you determine the formula for the graph of an exponential function given (0,2) and (3,1)?
- How do you state two equations for an exponential function that passes through (0,12) and shows growth?
- How do you state an equation for an exponential function that passes through (0,7) and shows decay?
- How would you find P and A of the equation f(x)=PA^x given f(2)=5400 and f(6)= 345000?
- How do you write an exponential function to model each situation & solve given the population of Warren Michigan was 145,600 in 1990. If the population decreases by 1.2% each year, predict the population in 1999?
- How do you write an exponential function to model each situation & solve given whole milk consumption in the U.S. has decreased by 4% annually since 1985. Each person consumed 13.6 gallons of whole milk in 1985. Predict whole milk consumption in 2000?
- What is the domain of f(x) = (-2)^x?
- Why is x^-3 not a Exponential Function?
- Which is an exponential function f(x)=x^3 or g(x)=3^x?
- How do you write an exponential function of the form y = a b^x the graph of which passes through (-1, 4/5) and (2, 100)?
- How do you find formula for the exponential function in the form of f(x)= Ca^x given f(0)=3 and f(1)=15?
- The half life of the radioactive element Strontium-90 is 37 years. In 1950, 15 kilograms of this element released accidentally. How do you determine the formula which shows the mass remaining after t years?
- A lab has 40 kg of radioactive uranium this substance has a half-life of 8 minutes and decays exponentially. How do you find the decay constant k?
- How do you find the y-intercept of #y=10(4^x)#?
- If 2^x = 3, what does 4^(-x) equal?
- If #5^(-x) = 3#, what does #5^(3x)# equal?
- How do you find an exponential function of the form f(x)=ab^x that has the given y-intercept (0,5); passing through P=(2, 5/9)?
- How do you find an exponential function of the form f(x)=ab^x that has the given y-intercept (0,2); passing through P=(-1, 2/5)?
- How do you find formulas for the exponential functions satisfying the given conditions h(0)=3 and h(1)= 15?
- How do you find formulas for the exponential functions satisfying the given conditions f(3)=-3/8 and f(-2)=-12?
- How do you find formulas for the exponential functions satisfying the given conditions g(1/2)=4 and g(1/4)=2sqrt2?
- A serving of a popular cola soft drink has 46 mg of caffeine. Suppose the half-life for caffeine remaining in he body of a typical adult is 6 h. How do you write an exponential decay function that gives the amount of caffeine in the body after t hours?
- How do you find the exponential function f(x) = Ca^x whose graph has the given points. (2,0) and (2,2/9)?
- How do you find the exponential function f(x) = Ca^x whose graph has the given points (0,2) and (3,54)?
- Radium-221 has a half-life of 30 seconds. How long will it take for 94% of a sample to decay?
- If 250 mg of a radioactive element decays to 220 mg in 12 hours, how do you find the half-life of the element?
- The half-life of radium is 1590 year. If 10 grams is present now, how much will be present in 50 years?
- Use the exponential decay model, A=Aoe^(kt), to solve this exercise. The half-life of polonium-210 is 140 days. How long will it take for a sample of this substance to decay to 20% of its original amount?
- A population P is initially 1000. How do you find an exponential model (growth or decay) for the population after t years if the population P is increases by 200% every 6 years?
- The value of an industrial machine has a decay factor of 0.75 per year. After six years, the machine is worth 7500. What was the original value of the machine?
- In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model A = 1900e^(0.058t). By what percentage is the account increasing each year?
- A population P is initially 3000. How do you find an exponential model (growth or decay) for the population after t years if the population P is multiplied by 0.65 every month?
- The half-life of cobalt 60 is 5 years. How do you obtain an exponential decay model for cobalt 60 in the form Q(t) = Q0e^−kt?
- How do you find the associated exponential decay model given Q = 100 when t = 0; Half-life = 6?
- Population in 1990 was 643 million. By 2000, it had grown to 813 million. HOw do you find the exponential growth model?
- The half-life of iodine-131 is 7.2 days. How long will it take for a sample of this substance to decay to 30% of its original amount?
- A used car has a value of $15,250 when it is purchased in 2012. The value of the car depreciates at a rate of 7.5% per year. How do you write an exponential function that models the value of the car, y, over x years?
- The function #f(x) = 200 × (1.098)^x# represents a village's population while it is growing at the rate of 9.8% per year. How do you create a table to show the village's population at 0, 2, 4, 6, 8, and 10 years from now?
- A sample of 2100 bacteria selected from this population reached the size of 2169 bacteria in one and a half hours. How do you find the hourly growth rate parameter?
- You Buy a Commemorative coin for $110. Each Year (t) the value (v) of the coin increases by 4%. Write an exponential model for this situation. Calculate the value of the coin after 3 years. When will the value of the coin will be $150?
- A bacteria culture starts with 2,000 bacteria and doubles in size every 3 hours. How do you find an exponential model for the size of the culture as a function of time t in hours?
- How do you find the exponential model #y=ae^(bx)# that goes through the points (4,256) (3,64)?
- A bacteria culture starts with 1,500 bacteria and doubles in size every 2 hours. How do you find an exponential model for the size of the culture as a function of time t in hours?
- How do you find the exponential model #y=ae^(bx)# that goes through the points (1, 1.2) and (4, 0.0768)?
- A bacterial culture starts with 2,000 bacteria and doubles in size every 6 hours. How do you find an exponential model for the size of the culture as a function of time t in hours?
- How do you find the exponential model #y=ae^(bx)# that goes through the points (0,7) (5, 32)?
- How do you find the exponential model #y=ae^(bx)# that goes through the points (2,8) (6, 128)?
- How do you find the exponential model #y=ae^(bx)# that goes through the points (-3,2)(1,164)?
- How do you find the exponential model #y=ae^(bx)# that goes through the points (-1,125) (2,5)?
- How do you find the exponential model #y=ae^(bx)# that goes through the points (-5, 243/2) and (-1, 3/2)?
- How do you find the exponential model #y=ae^(bx)# that goes through the points (5,3200) and (11,6800)?
- The decay rate of a certain chemical is 9.8% per year what is the half life?
- How do you find the associated exponential decay or growth model: Q = 1,500 when t = 0; half-life = 1?
- The value of a new car bought for $20,000 decreased by 10% per year. How do you write an exponential decay model for the value of the car and use the model to estimate the value after one year?
- The population of the world in 1987 was 5 billion and the relative growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 1995?
- Question #ae84e
- What is an example of a value of b for which #y=b^x# represents an exponential decay?
- How do you graph #y=5^x#?
- How do you graph #y=2(5)^x#?
- How do you graph #y=3(4)^x# and state the domain and range?
- How do you graph #y=(0.5)^x# and state the domain and range?
- How do you graph #y=0.3(5)^x# and state the domain and range?
- How do you write an exponential function whose graph passes through the points (0,3) and (-1,6)?
- How do you write an exponential function whose graph passes through the points (0,-18) and (-2,-2)?
- How do you simplify #2^sqrt7*2^sqrt7#?
- How do you simplify #(a^pi)^4#?
- How do you simplify #81^sqrt2 div 3^sqrt2#?
- How do you graph of #y=2(3)^x# and state the domain and range?
- How do you graph of #y=5(2)^x# and state the domain and range?
- How do you graph of #y=-(1/5)^x# and state the domain and range?
- How do you determine if #y=2(4)^x# is an exponential growth or decay?
- How do you determine if #y=0.4(1/3)^x# is an exponential growth or decay?
- How do you determine if #y=3(5/2)^x# is an exponential growth or decay?
- How do you determine if #y=30^-x# is an exponential growth or decay?
- How do you determine if #y=0.2(5)^-x# is an exponential growth or decay?
- How do you write an exponential function whose graph passes through (0,3) and (1,15)?
- How do you write an exponential function whose graph passes through (0,7) and (2,63)?
- How do you write an exponential function whose graph passes through (0,-5) and (-3, -135)?
- How do you write an exponential function whose graph passes through (0,0.2) and (4, 51.2)?
- How do you write an exponential function whose graph passes through (0,-0.3) and (5,-9.6)?
- How do you simplify #(5^sqrt2)^sqrt8#?
- How do you simplify #(x^sqrt5)^sqrt3#?
- How do you simplify #7^sqrt2*7^(3sqrt2)#?
- How do you simplify #y^(3sqrt3)divy^sqrt3#?
- How do you simplify #n^2*n^pi#?
- How do you simplify #64^pidiv2^pi#?
- How do you graph #y=3^x# and #y=3^(x+1)# and how do the graphs compare?
- How do you graph #y=(1/5)^x# and #y=(1/5)^(x-2)# and how do the graphs compare?
- How do you graph #y=(1/4)^x# and #y=(1/4)^x-1# and how do the graphs compare?
- What are the effect of changing the values of h and k in the equation #y=2^(x-h)+k#?
- How do you simplify #(b^sqrt6)^sqrt24#?
- A country's population in 1994 was 195 million. In 2002 it was 199 million. How do you estimate the population in 2016 using the exponential growth formula #P=Ae^(kt)#?
- How do you find the equation of the exponential function #y=a(b)^x# which goes through the points(2, 18) and (6,91.125). What is the intercepts of this function?
- The initial population of a large city is #20# million. Its population increases by 2% each year. It's 2012 today. How many people will live in the city at the end of 2016?
- The exponential function #f(x)= 15,000(1.02)^x# models the amount of money in a savings account over a period of time. What does the value 15,000 represent?
- How do you find the annual percent increase or decrease that #y =0.35(2.3)^x# models?
- A biologist studying a population of geckos for several years found that the population can be modeled as where #P# is the population, and #t# is in the time in years. # P= 230( 1.04)^t# . What is the growth rate of this population?
- How do you evaluate the function #f(x)=2.3^x# at the value of #x=3/2#?
- How do you evaluate the function #f(x)=5^x# at the value of #x=-pi#?
- How do you evaluate the function #g(x)=5000(2^x)# at the value of #x=-1.5#?
- How do you evaluate the function #h(x)=e^-x# at the value of #x=3/4#?
- How do you evaluate the function #f(x)=e^x# at the value of #x=3.2#?
- How do you write the exponential functions goes through the points (1, 6) and (2, 12)?
- How do you graph and determine if #y=(4/3)^x# is a growth or decay?
- Question #553c3
- How do you tell whether #f(x)=(5/6)^x# is an exponential growth or decay?
- How do you tell whether #f(x)=(6/5)^x# is an exponential growth or decay?
- How do you tell whether #f(x)=(5/6)^-x# is an exponential growth or decay?
- How do you tell whether #f(x)=(6/5)^-x# is an exponential growth or decay?
- How do you tell whether #f(x)=-(6/5)^-x# is an exponential growth or decay?
- How do you graph, find any intercepts, domain and range of #f(x)=(1/4)^(x+3)-2#?
- How do you graph, find any intercepts, domain and range of #f(x)=4(1/2)^(x-1)-3#?
- How do you graph, find any intercepts, domain and range of #f(x)=(1/4)^(x+4)-3#?
- How do you graph, find any intercepts, domain and range of #f(x)=-(3/4)^(x+2)+5#?
- An exponential function passes through the points #(-3, 8)# and #(0, 1)#. What is the equation of the function?
- Question #2720a
- A population of rabbits follows the law of uninhibited growth. There are 5 rabbits initially and after 4 months there are 35. a.) How many rabbits will there be in one year? b.) How long will it take for the initial population to triple?
- When a living organism dies, the amount of Carbon-14 in its system begins to decrease exponentially. Given that the half-life of Carbon-14 is 5,730 years, answer the following: a.) What is the exact value of the rate of decay for Carbon-14?
- Question #e84e3
- Question #16386
- Question #72ac5
- The number of mold spores in a petri dish increases by a factor of 10 every week. If there are initially 40 spores in the dish, how long will it take for there to be 2000 spores?
- The value of a machine depreciate each year by 5% of its value at the beginning of that year. If its value when new on first 1968 was 10250,what was its value in January 1978?