Answer:
[tex]y =120*1.1^x[/tex]
[tex]r = 10\%[/tex] --- Percentage increase
Step-by-step explanation:
Given
Let
[tex]x \to months[/tex]
[tex]y \to mice[/tex]
So, we have:
[tex](x_1,y_1) = (0,120)[/tex] --- Monday
[tex](x_2,y_2) = (1,132)[/tex] --- One month later
Required
The function
The function is represented as:
[tex]y = ab^x[/tex]
In [tex](x_1,y_1) = (0,120)[/tex], we have:
[tex]120 =a * 1[/tex]
[tex]120 =a[/tex]
Rewrite as:
[tex]a = 120[/tex]
In [tex](x_2,y_2) = (1,132)[/tex], we have:
[tex]132 = a * b^1[/tex]
[tex]132 = a * b[/tex]
Substitute [tex]a = 120[/tex]
[tex]132 = 120 * b[/tex]
Solve for b
[tex]b = \frac{132}{120}[/tex]
[tex]b = 1.1[/tex]
Recall that:
[tex]y = ab^x[/tex]
Hence, the function is:
[tex]y =120*1.1^x[/tex]
To get the monthly percentage increase (r), we have:
[tex]y = a(1 + r)^x[/tex]
Compare to: [tex]y = ab^x[/tex]
So:
[tex]1+r =b[/tex]
Make r the subject
[tex]r = b-1[/tex]
[tex]r = 1.1-1[/tex]
[tex]r = 0.1[/tex]
Express as percentage
[tex]r = 0.1*100\%[/tex]
[tex]r = 10\%[/tex]
