Question

Which function represents the same relationship?

a. f(x) = 15(5/6)^x
b. f(x) = 18(6/5)^x
c. f(x) = 15(6/5)^x
d. f(x) = 18(5/6)^x

Answer 1

B

Explanation:

We can use the standard form of an exponential function:

`y=a(b)^x`

The point (0, 18) tells us that y = 18 when x = 0. Hence:

`\displaystyle 18=a(b)^0`

Simplify:

`a=18`

Our equation is now:

`\displaystyle y=18(b)^x`

Next, the point (-1, 15) tells us that y = 15 when x = -1. Hence:

`15=18(b)^(-1)`

Isolate the variable:

`\displaystyle (1)/(b)=(5)/(6)`

Hence:

`\displaystyle b=(6)/(5)`

By substitution:

`\displaystyle y=18\left((6)/(5)\right)^x`

Our answer is B.