Question

16

Answer 1

Answer:

$2.50$

Step-by-step explanation:

Given

$(x_1,y_1) = (-1,0.8)$

$(x_2,y_2) = (0,2)$

$(x_3,y_3) = (1,5)$

$(x_4,y_4) = (2,12.5)$

Required

The rate of change (b)

The above graph is represented as:

$y = ab^x$

For: $(x_2,y_2) = (0,2)$;

We have:

$y = ab^x$

$2 = a * b^0$

$2 = a *1$

$2 = a$

$a = 2$

For $(x_3,y_3) = (1,5)$,

We have:

$y = ab^x$

$5 = a * b^1$

$5 = a * b$

Substitute $a = 2$

$5 = 2 * b$

Divide by 2

$2.5 = b$

$b = 2.5$

Hence, the rate of change is 2.50