Question

Which of the following options results in a graph that shows exponentialdecay?5 pointsO f(x) 0.4(0.2)^xf(x) = 4(4)^xf(x) = 0.7(1.98)^xOf(x) = 5(1+.1)^x

Answer 1

Option A is the answer.

f(x) = 0.4(0.2)ˣ

The value carrying the power of x is less than 1, so, this expression represents exponential decay.

Step-by-step explanation

The key to knowing which expression is represents an exponential decay or exponential growth is the value of the number carrying the power of x.

If that number is greater than 1, then it represents exponential growth.

But, if that number is lesser than 1 (but greater than 0), then it represents exponential decay.

(2)ˣ represents exponential growth.

(0.5)ˣ represents exponetial decay.

f(x) = 0.4(0.2)ˣ

The value carrying the power of x is less than 1, so, this expression represents exponential decay.

f(x) = 4(4)ˣ

The value carrying the power of x is greater than 1, so, this expression represents exponential growth.

f(x) = 0.7(1.98)ˣ

The value carrying the power of x is greater than 1, so, this expression represents exponential growth.

f(x) = 5(1 + .1)ˣ

The value carrying the power of x is greater than 1, so, this expression represents exponential growth.

Hope this Helps!!!