Question

A population of mice is increasing exponentially. On Monday there were 120 mice. One month later there were 132 mice. Write a function to model this situation. Determine the percent increase of the population of mice each month.

Answer 1

Answer:

$y =120*1.1^x$

$r = 10\%$ --- Percentage increase

Step-by-step explanation:

Given

Let

$x \to months$

$y \to mice$

So, we have:

$(x_1,y_1) = (0,120)$ --- Monday

$(x_2,y_2) = (1,132)$ --- One month later

Required

The function

The function is represented as:

$y = ab^x$

In $(x_1,y_1) = (0,120)$, we have:

$120 =a * 1$

$120 =a$

Rewrite as:

$a = 120$

In $(x_2,y_2) = (1,132)$, we have:

$132 = a * b^1$

$132 = a * b$

Substitute $a = 120$

$132 = 120 * b$

Solve for b

$b = \frac{132}{120}$

$b = 1.1$

Recall that:

$y = ab^x$

Hence, the function is:

$y =120*1.1^x$

To get the monthly percentage increase (r), we have:

$y = a(1 + r)^x$

Compare to: $y = ab^x$

So:

$1+r =b$

Make r the subject

$r = b-1$

$r = 1.1-1$

$r = 0.1$

Express as percentage

$r = 0.1*100\%$

$r = 10\%$