The population of a town grew from 20,000 to 28,000. the continuous growth rate is 15%. the equation 20,000e^0.15t=28,000 represents the situation, where t is the number of years the population has been growing. about how many years has the population of the town been growing? use a calculator and round your answer to the nearest whole number. a. 2 years b.9 years c. 17 years d. 22 years

The correct option is:  A.  2 years

Explanation

The given growth equation is:   , where   is the number of years the population has been growing.

For finding the number of years, we will solve the above equation for  .

First, dividing both sides by 20000, we will get........

Now taking 'natural log' on both sides, we will get........

So, the population of the town has been growing about 2 years.

The town has been growing for 17 years

Given the exponential function

Given the expressions 20,000e^0.15t=28,000

We are to find the value of "t" which is the time.

e^0.15t = 28000/20000

e^0.15t = 7/5

e^0.15t = 1.4

Take the ln of both sides

lne^0.15t = ln 1.4

0.15t = 2.639

t = 2.639/0.15

t = 17years

Hence the town has been growing for 17 years

Learn more on exponential functions here: link

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>