MATH SOLVE

4 months ago

Q:
# 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 yearsB.9 yearsC. 17 yearsD. 22 years

Accepted Solution

A:

The correct option is: A. 2 yearsExplanationThe given growth equation is: [tex]20000e^0^.^1^5^t = 28000[/tex], where [tex]t[/tex] is the number of years the population has been growing. For finding the number of years, we will solve the above equation for [tex]t[/tex]. First, dividing both sides by 20000, we will get........[tex]\frac{20000e^0^.^1^5^t}{20000}=\frac{28000}{20000}\\ \\ e^0^.^1^5^t = 1.4[/tex]Now taking 'natural log' on both sides, we will get........[tex]ln(e^0^.^1^5^t)=ln(1.4)\\ \\ 0.15t*ln(e)= ln(1.4)\\ \\ 0.15t*1=ln(1.4)\\ \\ t=\frac{ln(1.4)}{0.15}=2.243..... \approx 2[/tex]So, the population of the town has been growing about 2 years.