Question

An exponential function is graphed in the xy-plane. If the graph of the function is always decreasing and has a y-intercept of 20, which of the following could be the function's equation?

A. y = -20(1.75)^x

B. y = 20(1.75)^x

C. y = -20(0.75)^x

D. y = 20(0.75)^x

Answer 1

D. y = 20(0.75)^x,
for function to be decreasing value under exponent should be less than 1,
y(int) can be found when x=0
y = 20(0.75)^0=20*1=20

Answer 2

The correct option is D.

Explanation:

The general exponential function is defined as

`f(x)=ab^x`

Where, a is the initial value and b is the growth factor.

→ If b>1, then it is a growth function and if b<1, then it is a decay function.

The function is always decreasing and has a y-intercept of 20. It means the initial value of function is 20.

Since the function is decreasing, therefore the value of growth factor must be less than 1.

In option A and C the initial value is 20, therefore options A and C are incorrect.

In option B,

`y=20(1.75)^x`

Growth factor is 1.75>1, therefore option B is incorrect.

In option D,

`y=20(0.75)^x`

Growth factor is 0.75<1, therefore option D is correct.