Question

1. choose the correct answers.

the mouse population in a certain building is 2,500 and is decreasing by 10% each week.
write a model for this situation.
using this model, how many mice were present after 3 weeks?
how many mice were present after 52 weeks (one year)?
a. 10 mice
b. 2 mice
c. $a(t) = 2,500(0.10)^t$
d. 1,822 mice
e. $a(t) = 2,500(0.9)^t$

Explanation:

Step1: Identify decay model formula

This is exponential decay, where the remaining population each week is \(100\% - 10\% = 90\% = 0.9\). The general form is \(A(t) = A_0(1-r)^t\), where \(A_0=2500\), \(r=0.10\).
<Expression>
\(A(t) = 2500(0.9)^t\)
</Expression>

Step2: Calculate population after 3 weeks

Substitute \(t=3\) into the model.
<Expression>
\(A(3) = 2500(0.9)^3 = 2500 \times 0.729 = 1822.5 \approx 1822\)
</Expression>

Step3: Calculate population after 52 weeks

Substitute \(t=52\) into the model.
<Expression>
\(A(52) = 2500(0.9)^{52} \approx 2500 \times 0.00081 = 2.025 \approx 2\)
</Expression>

Answer:

Write a model for this situation: e. \(A(t) = 2,500(0.9)^t\)
Using this model, how many mice were present after 3 weeks? d. 1,822 mice
How many mice were present after 52 weeks (one year)? b. 2 mice