Question

A population of a certain species of bat is 9,000 animals and is increasing at the rate of 7% annually. This paragraph describes a(n) scenario. Write an equation for y, the population at time t (in years), representing the situation.

Answer 1

The equation to model the population growth of bats increasing at a 7% annual rate is y = 9000(1 + 0.07)^t. This represents exponential growth, with y being the population at time t, P being the initial population size, r the growth rate, and t the time in years.

Step-by-step explanation:

To represent the population growth of bats that is increasing at a 7% annual rate, we can use the formula for exponential growth:

y = P(1 + r)^t

Where:

P is the initial population size,

r is the growth rate as a decimal,

t is the time in years,

y is the population at time t.

In this case, since the initial population (P) is 9,000 bats and the growth rate (r) is 7%, which is 0.07 as a decimal, the equation would be:

y = 9000(1 + 0.07)^t

This equation models the exponential growth of the bat population over time.