Question

For each function below, identify and enter the percent rate of change per unit, t. Round to the nearest tenth of a percent.

Answer 1

Answer:

Step-by-step explanation:

Expression that defines a growth function is,

$f(x)=a(1+r)^t$

Here, $a=$ initial amount

$r=$ growth rate

And $(1+r)$ = Growth factor

Similarly, decay function is represented by the expression,

$f(x)=a(1-r)^t$

That means if a function has a growth factor (1 + r) or greater than 1, function will have a exponential growth.

And a function with growth factor between 0 to 1, it will be a decay.

1). $f(t)=1.18^t$

  $f(t)=(1+\frac{18}{100})^t$

  Growth rate = 18%

  Here, 1.18 > 1

  Therefore, function is a growth function.

2). $g(t)=2^{-2t}$

    $g(t)=(2^{-2})^t$

    $g(t)=(\frac{1}{2})^t$

    $g(t)=(0.5)^t$

    $g(t)=(1-\frac{50}{100})^t$

    Decay rate = 50%

    Here growth factor (0.5) is less than 1.

    Therefore, function is a decay function.

3). $h(t)=1.19^\frac{t}{10}$

    $h(t)=(1.19^{\frac{1}{10}})^t$

           $=1.017^t$

           $=(1+0.017)^t$

           $=(1+\frac{1.7}{100})^t$

     Growth rate = 1.7%

     Growth factor (1.19) is greater than 1.

     Therefore, function will be a growth function.

4). $k(t)=0.13^t$

           $=(1-0.87)^t$

           $=(1-\frac{87}{100})^t$

    Decay rate = 87%

    Growth factor (0.13) < 1

    Therefore, function will be a decay function.