Question

what is the percent rate of change in function y = (0.98) ^ x? determine whether the function represents exponential growth or exponential decay​

Answer 1

C. 2%; exponential decay

Answer 2

You can use the fact that increasing power of values lying between 0 and 1 results in less and less values.

The percent rate of change in given function is -2%

The function represents exponential decay.

Given that:

• The function: $y = (0.98) ^ x$

To find:

• Percent rate of change in given function.
• Is it representing exponential growth or exponential decay?

Finding percent rate of change in given function:

For finding this, first find how much the output y changes if we change x from x to x + 1.

Output when x = x:   $y = (0.98)^x$

Output when x = x+1:  $y = (0.98)^{x+1}$

Difference in output if x goes from x to x+1: $(0.98)^{x+1} - (0.98)^x = (0.98)^x(0.98 - 1) = -0.02 \times (0.98)^x$ (this change occurs if we increase input x by 1 unit, thus this also represents the rate)

Rate of change of function per unit increment = $-0.02 \times (0.98)^x$

The percentage of rate of change is found as:

$\text{Percent rate of change\:} = \dfrac{\text{Rate of change} \times 100}{\text{previous value}} = \dfrac{-0.02 \times (0.98)^x \times 100}{(0.98)^x} \\\\ \text{Percent rate of change\:} = -2\%$

Thus, the percent rate of change is -2%

The negative sign shows that the value is decreasing, thus showing that function shows exponential decay.

Learn more about exponential growth or decay here:

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