Chapter 6, Problem 1RE

Determine whether the function $y=156{\left(0.825\right)}^t$ represents exponential growth exponential decay, orneither. Explain

To determine

The function represents exponential growth, exponential decay or neither.

Answer to Problem 1RE

The function $y=156{\left(0.825\right)}^t$exponential decay.

Explanation of Solution

Given:

The function $y=156{\left(0.825\right)}^t$

Formula used:

$y=a{\left(b\right)}^x$

Calculation:

We are given a function $y=156{\left(0.825\right)}^t$. It is a exponential function like $y=a{\left(b\right)}^x$

Where,

• $a$is initial value of function.
• $b$is rate of exponential function.
• If $b>1$then function exponential growth.
• If $0<b<1$then function exponential decay
• If $b<0$then function neither decay nor growth.

If we compare $y=156{\left(0.825\right)}^t$with $y=a{\left(b\right)}^x$

The value of $b=0.825$which is less than 1.

Hence, The function $y=156{\left(0.825\right)}^t$exponential decay.