Question

An initial population of 650 monkeys increases at an annual rate of 10%. Write an exponential function to model the monkey population. What will the approximate population be after 6 years?

Answer 1

Answer:

Part 1) $y=650(1.1^x)$

Part 2) Approximate 1,152 monkeys

Step-by-step explanation:

Part 1) Write an exponential function to model the monkey population

we know that

The exponential function is of the form

$y=a(b^x)$

where

y is the population of monkeys

x is the number of years

a is the initial value or y-intercept

b is the base of the exponential function

r is the percent rate of change

we have

$a=650\ monkeys\\r=10\%=10/100=0.10$

$b=1+r=1+0.10=1.10$

substitute

$y=650(1.1^x)$

Part 2) What will the approximate population be after 6 years?

For x=6 years

substitute the value of x in the exponential equation

$y=650(1.1^6)=1,151.5\ monkeys$

Approximate 1,152 monkeys