Question

Which expression represents exponential decay

A. Y=1/100 (31)x

B. Y=1/10 (3.1)x

C. Y=10(0.13)x

D. Y=100(1.03)x

Answer 1

Given:

The exponential equations in the options.

To find:

The equation which represents exponential decay.

Solution:

The general exponential equation is

`y=ab^x`

where, a is initial value and b is growth rate.

If b<1, then it is an equation of exponential decay.

If b>1, then it is an equation of exponential growth.

In option A, b=31>1, i.e., exponential growth.

In option B, b=3.1>1, i.e., exponential growth.

In option C, b=0.13<1, i.e., exponential decay.

In option D, b=1.03>1, i.e., exponential growth.

Only
`y=10(0.13)^x` represents exponential decay.

Therefore, the correct option is C.