The value of b is closest to (2) 2.25
An exponential function is represented as:
[tex]f(x) = a(b)^x[/tex]
[tex]f(5) = 15[/tex] means that:
[tex]ab^5 = 15[/tex] ---- equation (1)
[tex]f(8) = 170[/tex] means that:
[tex]ab^8 = 170[/tex] ---- equation (2)
Divide equation (2) by equation (1)
[tex]\frac{ab^8}{ab^5}= \frac{170}{15}[/tex]
Divide common factors
[tex]b^3= 11.33[/tex]
Take the cube root of both sides
[tex]b= \sqrt[3]{11.33}[/tex]
Evaluate the expression
[tex]b= 2.246[/tex]
2.246 can be approximated to 2.25
Hence, the value of b is closest to (2) 2.25
Read more about exponential functions at:
https://brainly.com/question/11464095
