Question

Does each equation represent exponential decay or exponential growth?

Answer 1

An exponential equation is represented as: $\mathbf{y = ab^x}$, where b represents rate

• Exponential growth: $\mathbf{y = 5(7)^x}$,  $\mathbf{y = 3(4.2)^x}$ and $\mathbf{y = 0.6(1.3)^x}$
• Exponential decay: $\mathbf{k = 4.2(0.28)^x}$
• Neither: $\mathbf{h(x) - 3x + 1.3}$

An exponential equation is said to represent growth, if the rate is greater than 1, while it represents decay if the rate is less than 1.

This means that:

$\mathbf{y = 5(7)^x}$,  $\mathbf{y = 3(4.2)^x}$ and $\mathbf{y = 0.6(1.3)^x}$ represent exponential growth because 5, 4.2 and 1.3 are greater than 1

Also,

$\mathbf{k = 4.2(0.28)^x}$ represents exponential decay because 0.28 is less than 1

While

$\mathbf{h(x) - 3x + 1.3}$ is not an exponential function

Read more about exponential functions at:

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