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# Determine whether each equation represents exponential growth or exponential decay. Find the rate of increase or decrease for each model. Graph each equation. y=5^x

Exponential growth and decay
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asked 2021-03-06

Determine whether each equation represents exponential growth or exponential decay. Find the rate of increase or decrease for each model. Graph each equation. $$y=5^x$$

## Answers (1)

2021-03-07

Given: $$\displaystyle{y}={5}^{{x}}$$
Rewrite as: $$y = 1(5)^{x}$$
For a. function, $$y = ab^x$$,
- the function represents exponential growth if a > 0 and b > 1.
- the function represents exponential decay if a > 0 and b < 1.
In either case, the y-intercept is (0,2).
From the given, a = 1 and b = 5. Becatise a > 0 and b > 1, then the function represents an exponential growth and the y-intercept is (0,1)

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