Applications of Exponential Functions

Key Questions

• How do you know if a word problem is talking about exponential functions?

  Example:

  John tells you a secret. You see no harm in telling Bob and Rob .

  After this, 4 people know the secret (John, you Bob and Rob). Suppose that both Bob and Rob decide to tell the secret to two new people.

  After the third "round" of indiscretion, eight people will know the secret.

  If this pattern of spreading the secret continues, how many people will know the secret after 10 such "rounds"?

  Alex Boroda · 1 · May 18 2015
• How do you determine the exponential function for a half life problem?

  If half-life of a certain quantity #Q(t)# is #h#, then we can write

  #Q(t)=Q(0)(1/2)^{t/h}#.

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  Example

  Suppose that a certain radioactive substance has a half-life of 20 years. If you initially have 100 g of this substance, then find the quantity function #Q(t)# of this substance after #t# years.

  Since #Q(0)=100# and #h=20#, we have

  #Q(t)=100(1/2)^{t/20}#.

  ---

  I hope that this was helpful.

  Wataru · 2 · Nov 2 2014
• What are some Applications of Exponential Functions?

  Answer:

  Population growth

  Explanation:

  Population growth such as bacteria growth.

  Decay such as radioactive decay.

  Bill Jorgensen · 1 · Jun 6 2018

• How do you know if a word problem is talking about exponential functions?
• What are some Applications of Exponential Functions?
• What percent of a substance is left after six hours if a radioactive substance decays at a rate of 3.5% per hour?
• How many bird species will there be left in the year 2020 if in 1990, a rural area had 1200 bird species and are becoming extinct at the rate of 1.5% per decade (10 years)?
• What is the total amount in the account after 12 years if Peter invests $360 in an account that pays 7.25% compounded annually?
• How do you determine the exponential function for a half life problem?
• How many bacteria would be present 15 hours after the experiment began if a set of bacteria begins with 20 and doubles every 2 hours?
• How many bacteria will be present after 5 hours if a culture of bacteria obeys the law of uninhibited growth where if 500 bacteria are present in the culture initially and there are 800 after 1 hour?
• If the length of a side of a cube is 4x, what is the volume of the cube?
• Why can't you have zero to the power of zero?
• How do you find an expression for the population after t hours if a bacteria culture grows with constant relative growth rate and after 2 hours there are 600 bacteria and after 8 hours the count is 75000?
• How long will it take for his money to triple if Carl plans to invest $500 at 8.25% interest, compounded continuously?
• What speed is she certain never to exceed however far she falls if the speed of a skydiver in free fall is modeled by the equation v=50(1-e^-o.2t) where v is her speed in meters per second after t seconds?
• What was the yearly rate of appreciation if the Marriot family bought a new apartment three years ago for $65,000 and the apartment is now worth $86,515?
• How long will it take you to triple your money if you invest it at a rate 6% compounded annually?
• How do you calculate to the nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 3.8%?
• What is the half-life of the substance if a sample of a radioactive substance decayed to 97.5% of its original amount after a year? (b) How long would it take the sample to decay to 80% of its original amount? _______years??
• How do you find the value of your investment after five year's growth if you invest $2000 in a bank offering 10% interest compounded weekly?
• How do you find the number of bacteria after t hours if a bacteria culture contains 300 cells initially and grows at a rate proportional to its size and after two hours the population has increased to 420 cells?
• If the temperature of the turkey is 150°F after half an hour, what is the temperature after 55 minutes if you know roast turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 75°F?
• In how many years will the population of the city be #120,000# if the population #P# in thousands of a city can be modeled by the equation #P=80e^0.015t# , where t is the time in years?
• How do you find the size of the bacterial population after 100 minutes if a bacteria culture initially contains 1500 bacteria and doubles every half hour and the formula for the population is, #p (t) = 1500e^(kt)# for some constant, k ?
• How do you show that the temperature of the coffee after t minutes is #20 + 75e^(-kt)# if a cup of coffee has a temperature 95 degree Celsisus and takes 30 minutes to cool to 61 degrees celsisus in a room with temperature 20 degrees celsisus?
• What is the half-life of (Na^24) if a research assistant made 160 mg of radioactive sodium (Na^24) and found that there was only 20 mg left 45 h later?
• How do you identify equations as exponential growth, exponential decay, linear growth or linear decay #6x+5y=30#?
• How do you identify equations as exponential growth, exponential decay, linear growth or linear decay #y=(3/4)^3#?
• How do you identify equations as exponential growth, exponential decay, linear growth or linear decay #y=2x#?
• How do you identify equations as exponential growth, exponential decay, linear growth or linear decay #f(x) = 3 (1/2) ^2#?
• How do you identify equations as exponential growth, exponential decay, linear growth or linear decay #f(x) = 4 (3/2)^x#?
• How do you identify equations as exponential growth, exponential decay, linear growth or linear decay #M(t)=8(2)^(1/6t)#?
• How do you identify equations as exponential growth, exponential decay, linear growth or linear decay #f(x) = 9.6 ∙ 1.06x#?
• How do you determine if the equation #y = 5^x# represents exponential growth or decay?
• How do you determine if the equation #y = (0.3)^x # represents exponential growth or decay?
• How do you determine if the equation #y = 300(1.6)^x# represents exponential growth or decay?
• How do you determine if the equation #y = 50(0.03)^x # represents exponential growth or decay?
• How do you solve #5^x+1=625#?
• How do you solve for x?: log(x) - log(x-3)=-1
• What is x if #log5 x = -3#?
• What is x if #log(5x) = -3#?
• What is x if #-log(5x) = -3#?
• What is x if #ln(x^2-x)-ln(5x) = -3#?
• What is a natural log?
• What is x if #log_2(x)+Log_2(x-7)=3#?
• What is x if #log_4(100) - log_4(25) = x#?
• What is #e^(ln(x)#?
• What is #ln(e^x)#?
• What is #cos(ln(x))#?
• What is #cosh(ln(x))#?
• What is x if #log_2(x) + log_3(x + 1) = log_5(x - 4)#?
• How do you convert a logarithm to a different base?
• What is x if #log(7x-12) - 2 log(x)= 1 #?
• What is x if #log(7x-10) - 3 log(x)= 2 #?
• Can you take the logarithm of a negative number?
• Can the logarithm of a number be negative? Can it be imaginary?
• What is x if #log_2(3-x) + log_2 (2-x) = log_2 (1-x)#?
• What is x if #ln(x^2) + ln(x^3) + 2 =0#?
• What is x if #ln(3x^2) + ln(x^4) + ln(7) =0#?
• What is x if #3log_8(x)=2log_8(x)+5#?
• What is x if #log_4(16x) = 1/2#?
• What are the asymptotes of logarithmic functions?
• What is the inverse of a logarithmic function?
• How do you invert a logarithmic function?
• Are logarithmic functions one to one?
• Are exponential functions necessarily one to one?
• How do you find the inverse of an exponential function?
• WHat is x if #3log_2 (x+1) = 15#?
• What is x if #3log_2 (x+1) = 15#?
• What is x if #lnx + ln5x^2 = 10#?
• What is x if #log_4(8x ) - 2 = log_4 (x-1)#?
• What is x if #log_2 (x+5) - log_2(x-2) +2= 3#?
• What is x if #log_4 x=2 - log_4 (x+6)#?
• What is x if #log_3 (2x-1) = 2 + log_3 (x-4)#?
• What is x if #log_4 x= 1/2 + log_4 (x-1)#?
• What is x if #log_3 (x-1) + log_3 (x-9) = 2#?
• What is x if #log_8(1-x) + (10log_32(x))/3-log_2(e^ln(1/x)/3)=4/3#?
• What is the solution to the following system of equations?:# log6 + log(x-3) = 2logy, 2y - x = 3#
• Why is #3*ln(x) = ln(x^3)#?
• How do you solve #8=(1/4)^x#?
• How do you solve #64 = 2^(3x)#?
• Composite function : If #f(x)= 3x+1# and #g(x) = x/(x^2+25)#, how to solve #g(f(x))=0# ?
• How do a construct an exponential equation given (0, -1) and (2, -36)?
• Question #d2b8e
• Question #25380
• Question #2aea5
• Question #92b81
• Question #b1a93
• Find the minimum value of #log_2^2 2 + log_ 2^3 2^2 + log_ 2^4 2^3.............log_2^n 2^(n-1)#?
• Why does a byte consist of #8# bits?
• How do you solve #3^(2x+1) = 5#?
• How do you solve #2e^(12x) = 18#?
• A scientist notes the bacteria count in a petrie dish is 50. Two hours later, he notes the count has increased to 80. If this rate of growth continues, how much more time will it take for the bacteria count to reach 100?
• How does #y=5^(x+1) - 2# relates to its parent function?
• The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years. How do you write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years?
• Evaluate #log_5(10)xxlog_5(x)=log_5(100)#?
• How do you prove that the 4-sd approximation to the value of #log_2(2+1/log_2(2+1/log_2(2+...)))# is 1.428?
• #F( x ; b) = log_b(x+1/log_b(x+1/log_b(x+...))), x>=b>1.#How do you approximate F(15, 10)=1.19958, nearly?
• On the scaling power of logarithmic FCF: #log_(cf) (x;a;b)=log_b (x+a/log_b(x+a/log_b (x+...))), b in (1, oo), x in (0, oo) and a in (0, oo)#. How do you prove that #log_(cf) ( "trillion"; "trillion"; "trillion" )=1.204647904#, nearly?
• FCF (Functional Continued Fraction) #cosh_(cf) (x; a)=cosh(x+a/cosh(x+a/cosh(x+...)))# How do you prove that #y = cosh_(cf) (x; x)# is asymptotic to #y = cosh x#, as #x -> 0# or the graphs touch each other, at #x = 0#?
• The FCF (Functional Continued Fraction) #cosh_(cf) (x;a)=cosh (x+a/cosh(x+a/cosh(x+...)))#. How do you prove that this FCF is an even function with respect to both x and a, together?and #cosh_(cf) (x; a) and cosh_(cf) (-x;a)# are different?
• Using Chebyshev Polynomial #T_n (x)=cosh( n( arc cosh(x))), x > = 1# and the recurrence relation #T_(n+2)(x)=2xT_(n+1)(x) - T_n (x)#, with #T_0(x)=1 and T_1(x)=x#, how do you porve that #cosh(7 arc cosh(1.5))=421.5?#
• #T_n(x)# is the Chebyshev polynomial of degree n. The FCF #cosh_(cf )(T_n (x); T_n (x))=cosh(T_n(x)+(T_n(x))/cosh(T_n (x) + ...)), x >= 1#. How do you prove that the 18-sd value of this FCF for #n=2, x =1.25# is #6.00560689395441650?
• A Functional Continued Fraction ( FCF ) is #exp_(cf)(a;a;a)=a^(a+a/a^(a+a/a^(a+...))), a > 1#. Choosing #a=pi#, how do you prove that the 17-sd value of the FCF is 39.90130307286401?
• Question #f669d
• Question #0a23d
• Question #961df
• Hello friends, please, I need to know how to get the answer out of this exponential equation? thank you
• Hello friends, please, I need to know how to get the answer out of this exponential equation? thank you
• How do I solve this? Thank you!
• How do you graph, find the intercepts and state the domain and range of #f(x)=6^x+3#?
• How do you graph, find the intercepts and state the domain and range of #f(x)=2-2^x#?
• How do you graph, find the intercepts and state the domain and range of #f(x)=4^x+3#?
• How do you graph, find the intercepts and state the domain and range of #f(x)=1/2(2^x-8)#?
• Question #34d69
• Question #6a798
• Question #35320
• A firm producing positive amount gains by increasing its production. Whether it is true or false?
• The function #f(t)=Pe^(rt)# describes the amount #P# will become if invested for #t# years at #r%# per annum compounded continuously. If a sum becomes #$246.40# at #4%# in #4# years, what is the amount invested?
• Prove that #2(log_10 5-1)=log_10 (1/4)#?
• Question #b6464
• Question #6d96f
• Question #35427
• Question #f7aeb
• Question #dba1a
• Plot the graphs of?: #A=16000(1+0.08/12)^(12t)# #A=16000(1+0.09/4)^(4t)#
• Question #1b0f0
• What does #0.01/0 xx 100# equal?
• If #x+1/x=sqrt5#, find the value of #x^2+1/x^2#?
• Question #32dad