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Suppose the population of Florida increases by 1.31 % each year. A) What is the 1-year growth...

Question:

Suppose the population of Florida increases by {eq}1.31 \% {/eq} each year.

A) What is the {eq}1 {/eq}-year growth factor?

B) What is the {eq}4 {/eq}-year growth factor?

C) What is the {eq}7 {/eq}-year growth factor?

D) What is the {eq}7 {/eq}-year percent change?

Growth Factor:

Growth factor is often confused with growth rate. Growth rate is the number we add to one and raise to some number then multiplied to the principal. On the other hand, growth factor is automatically multiplied to the principal.

Answer and Explanation:

For an growth rate of {eq}1.31\% {/eq} pe year, the growth factor can be solved as

a

$$f=\left(1+\frac{1.31}{100}\right)^1 \\ $$

$$\boxed{f=1.0131} $$

b

$$f=\left(1+\frac{1.31}{100}\right)^4 \\ $$

$$\boxed{f \approx 1.05343} $$

c

$$f=\left(1+\frac{1.31}{100}\right)^7 \\ $$

$$\boxed{f \approx 1.09538} $$

d

The percent change is the the different of the future value and initial value divided by the initial value

$$\frac{1.09538-1}{1}\times 100\% $$

$$\boxed{p \approx 9.538 \%} $$


Learn more about this topic:

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Exponential Growth: Definition & Examples

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