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For each function below, identify and enter the percent rate of change per unit, t. Round to the nearest tenth of a percent.

Then use the drop-down menus to classify each as exponential growth or decay

For each function below identify and enter the percent rate of change per unit t Round to the nearest tenth of a percent Then use the dropdown menus to classify class=

Respuesta :

The percentage rate of change of the given functions is given by the

derivative of their natural logarithm.

Responses:

[tex]f(t) = 1.18^t[/tex]

  • 16.6%, exponential growth

[tex]g(t) = 2^{-2 \cdot t}[/tex]

  • -138.6%, exponential decay

[tex]h(t) = 1.19^{\frac{t}{10} }[/tex]

  • 1.7%, exponential growth

[tex]k(t) = 0.13^t[/tex]

  • -204%, exponential decay

Which method is used to determine the percentage rate of change?

The percentage rate of change can be presented as follows;

[tex]Percentage \ rate \ of \ change = \mathbf{100 \times \dfrac{d}{dt} ln \left(f(t)\right)}[/tex]

[tex]f(t) = \mathbf{ 1.18^t} \ gives;[/tex]

  • [tex]100 \times \dfrac{d}{dt} \left( ln \left(1.18^t\right) \right) = \mathbf{ 100 \times ln(1.18)} \approx \underline{16.6\%}[/tex], exponential growth

[tex]g(t) = \mathbf{2^{-2 \cdot t} }\ gives;[/tex]

[tex]100 \times \dfrac{d}{dt} \left( ln \left(2^{-2 \cdot t}\right) \right) = \mathbf{ 100 \times -2 \times ln(2)} \approx \underline{ -138.6 \%}[/tex] , exponential decay

[tex]h(t) = \mathbf{1.19^{\frac{t}{10} } }\ gives;[/tex]

[tex]100 \times \dfrac{d}{dt} \left( ln \left(1.19^{\frac{t}{10} }\right) \right) = \mathbf{ 100 \times \dfrac{10 \cdot ln(1.19)}{100}} \approx 1.7 \%[/tex], exponential growth

[tex]k(t) = \mathbf{ 0.13^t} \ gives;[/tex]

[tex]100 \times \dfrac{d}{dt} \left( ln \left(0.13^t }\right) \right) = \mathbf{100 \times ln(0.13)}\approx -204 \%[/tex], exponential decay

Learn more about exponential functions here:

https://brainly.com/question/14325265

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