Question

An exponential function of the form ya(b) passes through the points (0.8) and (5,72). Which of the

following is the value of b to the nearest hundredth?
(1) 1.37
(2) 1.41
3) 1.48
4) 1.55

Answer 1

72 = 8b^5

B^5 = 72/8 = 9
Ln b^5 = Ln 9
5 Ln b = Ln 9
Ln b = ln 9 / 5
B = 1.5518
= 1.55

Answer 2

Explanation:

An exponential function is written as

`y=a(b)^x`

where a is the y-intercept

b is the factor of growth

Here, the y intercept is 8 since the point (0,8) indicates when x=0, the function is equal to 8.

So a=8

`y=8(b)^x`

To find b, we will use a little of algebraic manipulation

We know that

`72=8(b)^5\\9=b^5\\9^(1/5) =b\\`

Which is close to 1.55