Question

Does each function describe exponential growth or decay?

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Growth OR Decay

Answer 1

$y= ((1-0.002) ^{ \frac{1}{56}} ) ^{56t}= (0.998)^t$
Exponential Decay - because you are raising a number less than 1 to a power of time "t".
$y= ((1.008) ^{ \frac{1}{12}} ) ^{12t}= (1.008)^t$
Exponential Growth- because you are the number you are raising to the power of "t" is greater than 1.
$y=426(0.98)^{t}$
Exponential Decay- because (0.98) is less than 1.
$y=250(1 +0.004)^{t} = 250 (1.004)^t$
Exponential Growth- because 1004 is greater than 1 and being raised to the power of t; meaning that it will only increase as time increases.
$y= 12,000( \frac{1}{2})^{t}$
Exponential Decay - because you are raising one half(whihc is less than one) to the power of "t"; meaning that the value can only decrease with time increases.

Hope this helped!

Answer 2

The rates of an exponential function can either be growth or decay.

• $\mathbf{y = ((1 - 0.002)^{\frac{1}{56}})^{56t}}$, $\mathbf{y = 426(0.98)^t}$ and $\mathbf{y = 12000(\frac{1}{2})^t}$ represent decay
• $\mathbf{y = (1.008^\frac{1}{12})^{12t}}$ and $\mathbf{y = 250(1 + 0.004)^{t}}$ represent growth

An exponential function is represented as:

$\mathbf{y = ab^x}$

Where b represents the growth or decay of the function

When the rate of an exponential function is greater than 1. i.e. b > 1

Then the exponential function represents growth

When the rate of an exponential function is less than 1. i.e. b < 1

Then the exponential function represents decay

This means that, the following functions represent decay

$\mathbf{y = ((1 - 0.002)^{\frac{1}{56}})^{56t}}$

$\mathbf{y = 426(0.98)^t}$

$\mathbf{y = 12000(\frac{1}{2})^t}$

Because, they have a rate less than 1

While the following function, represent growth

$\mathbf{y = (1.008^\frac{1}{12})^{12t}}$

$\mathbf{y = 250(1 + 0.004)^{t}}$

Because, they have a rate greater than 1

Read more about exponential functions at:

https://brainly.com/question/3127939