# 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?

##### 2 Answers

Mar 29, 2015

We are given that

So

with a little help from Excel:

Mar 29, 2015

Approximately 27 years.

**I misread this question.**

**If** the the model is:

When the population is

We've been asked to solve:

Using a table of values or electronics gives an approximation of

**Notes:**

- Here I used
#ln# to mean the natural logarithm function. If your teacher or textbook uses#log# to mean the natural logarithm, then you should too. - When solving an exponential function, it is most convenient to start by making the form of the equation:
#"base"^"variable expression" = "constant expression"# . In this equation, that is the reason we divided by#80# before taking the natural logs of both sides of the equation.

#(# A constant expression is a number, like#1.5# or#3/2# or#(5+sqrt7)/8)#