Question

Which of the following does not represent exponential decay?

Answer 1

Answer:

y = 2(1 + 0.12)ˣ

Step-by-step explanation:

Exponential functions look like y = a(b)ˣ.

"x" and "y" would be points that are on the graph.

"a" is the y-intercept.

"b" is the rate of growth.

When "x" is positive in the equation:

"b" is greater than 1: exponential growth.

"b" is greater than 0 but less than 1: exponential decay.

Simplify each equation inside the brackets to find "b":

y = 2(1 + 0.12)ˣ

y = 2(1.12)ˣ

b = 1.12; b > 1; exponential growth.

y = 7(1 – 0.09)ˣ

y = 7(0.91)ˣ

b = 0.91; 0 < b < 1; decay

y = 0.63ˣ

b = 0.63; 0 < b < 1; decay

When "x" is negative (like in the last option):

b > 1 is exponential decay.

0 < b < 1 is exponential growth.

Since b = 2.42 when "x" is negative in the equation, y = 2.42⁻ˣ is a decay.