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2 years ago

Population in a Small Town, USA was 5,054 in 2007. The populations increase by 2% annually. Show and explain all work.

Mathematics

1 answer:

kakasveta [241]2 years ago

5 0

Answer: a. $f(x)=5054(1.02)^x$

b. The population in 2032 will be 8292.

Step-by-step explanation:

Exponential growth equation: $y=a(1+r)^x$ , where a = initial value , r = growth rate, x = time period

Given: a = 5054 , r= 0.02

a. Required exponential growth function: $f(x)=5054(1+0.02)^x$

$f(x)=5054(1.02)^x$

b. For 2032, x= 25

$f(25)=5054(1.02)^{25}$

$\approx8291.62\approx8292$

The population in 2032 will be 8292.

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Answer:

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Step-by-step explanation:

The null hypothesis is:

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Alternative hypothesis;

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$t= \dfrac{(9-6)-0}{\sqrt{7.14 ( \dfrac{1}{8} +\dfrac{1}{8})}}$

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Decision Rule: To reject the null hypothesis if the t-test is greater than the critical value.

Conclusion: We reject $H_o$ and there is sufficient evidence to conclude that the test scores for contact address s less than Noncontact athletes.

To calculate r²

The percentage of the variance is;

$r^2 = \dfrac{t^2}{t^2 + df}$

$r^2 = \dfrac{2.2450^2}{2.2450^2 + 14}$

$r^2 = \dfrac{5.040025}{5.040025+ 14}$

$r^2 = 0.2647$

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