Precalculus Textbook 8th Edition Section 3.2 Exercise 1-2-3 Solution

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Tell whether the function is an exponential growth function or exponential decay function, and the constant percentage rate of growth or decay.

Exercise 1: \[ p(t)=3.5\times 1.09^{t} \]

Exercise 2: \[ p(t)=4.3\times 1.018^{t} \]

Exercise 3: \[ p(t)=78963\times 0.968^{x} \]

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Solution:

In exponential population model, the base of the exponential term represents the exponential growth function or exponential decay function.

In exercise (1), \[ p(t)=3.5\times 1.09^{t} \].

The base of the exponential term is 1.09.

Since \[ p(t)=3.5\times 1.09^{t}\Rightarrow (1+r)=1.09\Rightarrow r=0.09>0 \]

Thus, the given function represents an Exponential Growth Function with 9% Growth.

In exercise (2), \[ p(t)=4.3\times 1.018^{t} \].

The base of the exponential term is 1.018.

Since \[ p(t)=4.3\times 1.0018^{t}\Rightarrow (1+r)=1.0018\Rightarrow r=0.018>0 \]

Thus, the given function represents an Exponential Growth Function with 1.8% Growth.

In exercise (3), \[ p(t)=78963\times 0.968^{x} \].

The base of the exponential term is 0.968.

Since \[ p(t)=78963\times 0.968^{t}\Rightarrow (1+r)=0.968\Rightarrow r=-0.032<0 \]

Thus, the given function represents an Exponential Decay Function with 3.2% Decay.

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