Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.

Question

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. $$ y=28(1.01)^{x} $$

UpStudy AI · Accepted Answer

The given exponential function is

$$
y = 28(1.01)^{x}.
$$

In this function, the base of the exponent is $$1.01$$. Since the base is greater than 1, this indicates that the function represents exponential growth.

To determine the percentage rate of increase, we can use the formula for the growth rate, which is given by:

$$
\text{Growth Rate} = (b - 1) \times 100\%
$$

where $$b$$ is the base of the exponential function. In this case, $$b = 1.01$$.

Calculating the growth rate:

$$
\text{Growth Rate} = (1.01 - 1) \times 100\% = 0.01 \times 100\% = 1\%.
$$

Thus, the change represents exponential growth, and the percentage rate of increase is $$1\%$$.
The function represents exponential growth with a rate of $$1\%$$.

Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.

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