Question

In Texas, the population of a species of bats is decreasing at a rate of -0.121 per year. The population was 34,000 in 2000. According to the function; A(t) = A0e^(kt), what is the predicted population in 2015?

Answer 1

A(t) = A0e^(kt)

A (t) ?
A0 34000
E constant
K -0.121
T 2015-2000=15 years

A (15)=34,000×e^(−0.121×15)=5,536

Answer 2

Population of bats in year 2015 is 5536.

Explanation:

The given function A(t) =
`A_(0)e^(-kt)` predicts the population of bats after t years.

Here A(t) = population after 't' years

k = growth constant

t = time in years

`A_(0)` = initial population

In year 2000 population of bats A(t) = 34,000

Since rate of decrease in population k = 0.121 per year

So population in 2015 will be

A(t)
`A_(0)e^((-0.121)(15))`

= 34,000 [
`e^(-1.815)` ]

= 34,000 ( 0.162837)

= 5536 bats

Therefore, population of bats in year 2015 is 5536.