Question

All of the functions shown below are either exponential growth or decay functions.

Complete the table by classifying each function as either growth or decay. Select Exponential Growth or Exponential Decay for each function.
Exponential Growth Exponential Decay
y = 3.2(1 + 0.45)2X
y = 2(0.85)3
y = (1 -0.03)* + 4
y = 0.5(1.2)* + 2
S
Help

Answer 1

Explanation:

If an exponential function is in the form of y = a(b)ˣ,

a = Initial quantity

b = Growth factor

x = Duration

Condition for exponential growth → b > 1

Condition for exponential decay → 0 < b < 1

Now we ca apply this condition in the given functions,

1).
`y=3.2(1+0.45)^(2x)`

Here, (1 + 0.45) = 1.45 > 1

Therefore, It's an exponential growth.

2).
`y=(0.85)^(3x)`

Here, (0.85) is between 0 and 1,

Therefore, it's an exponential decay.

3). y = (1 - 0.03)ˣ + 4

Here, (1 - 0.03) = 0.97

And 0 < 0.97 < 1

Therefore, It's an exponential decay.

4). y = 0.5(1.2)ˣ + 2

Here, 1.2 > 1

Therefore, it's an exponential growth.