Question

Indicate whether the function represents an exponential growth or decay.

Answer 1

1) decay

2) growth

3) growth

Explanation:

A generic exponential function can be written as:

f(x) = A*(r)^x

Where:

A is the initial amount of something.

r is the rate of growth.

x is the variable, usually, represents time.

if r > 1, we have an exponential growth.

if r < 1, we have an exponential decay.

1) f(x) = (3/4)^x

in this case we have:

A = 1

r = (3/4) = 0.75

Clearly, r < 1.

Then this is an exponential decay.

2) f(x) = (1/6)*4^x

In this case we have:

A = (1/6)

r = 4

Here we have r > 1.

Then this is an exponential growth.

3) f(x) = (1/4)*(5/2)^x

in this case we have:

A = 1/4

r = 5/2 = 2.5

here we have r > 1, then this is an exponential growth.