Question

The growth in the mouse population at a certain county dump can be modeled by the exponential function A(t)= 906e0.012t, where t is the number of months since the population was first recorded. Estimate the population after 36 months.

Answer 1

Answer:

$A(t) = 906 e^{0.012t}$

Where t is the number of months since the population was first recorded. And we want to find the population after 36 months so we need to replace t=36 months into the function and we got:

$A(36) = 906 e^{0.012*36}= 1395.54$

So then we can conclude that after 36 months the population of mouse is between 1385 and 1396.

Step-by-step explanation:

We know that the population can be represented with this formula:

$A(t) = 906 e^{0.012t}$

Where t is the number of months since the population was first recorded. And we want to find the population after 36 months so we need to replace t=36 monthsinto the function and we got:

$A(36) = 906 e^{0.012*36}= 1395.54$

So then we can conclude that after 36 months the population of mouse is between 1385 and 1396.