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2 years ago

A population numbers 15,500 and grows at 3.75% per year. Write an exponential model for the growth of this population.

Mathematics

1 answer:

krek1111 [17]2 years ago

4 0

Answer: $f(x)=15500(1.0375)^x$

Step-by-step explanation:

The exponential model for growth is given by :-

$f(x)=A(1+r)^x$ , where A = initial value , r = growth rate (in decimal), x = time (in years).

Given: A= 15,500 r= 3.75% = 0.0375

The exponential model for the growth of this population will be :

$f(x)=15500(1+0.0375)^x\\\\\Rightarrow\ f(x)=15500(1.0375)^x$

hence, the required model: $f(x)=15500(1.0375)^x$

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jonny [76]

Answer:

$t _{critical} = 1.760$

t = 2.2450

d. 0.264

Step-by-step explanation:

The null hypothesis is:

$H_o: \mu_1 - \mu_2 = 0$

Alternative hypothesis;

$H_a : \mu_1 - \mu_2 > 0\\$

The pooled variance t-Test would have been determined if the population variance are the same.

$S_p^2 = \dfrac{(n_1-1)S_1^2+(n_2-1)S^2_2}{(n_1-1)+(n_2-1)}$

$S_p^2 = \dfrac{(8-1)2.507^2+(8-1)2.8282^2}{(8-1)+(8-1)}$

$S_p^2 = 7.14$

The t-test statistics can be computed as:

$t= \dfrac{(x_1-x_2)-(\mu_1 - \mu_2)}{\sqrt{Sp^2 ( \dfrac{1}{n} +\dfrac{1}{n_2})}}$

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

$t= \dfrac{3}{1.336}$

t = 2.2450

Degree of freedom $df = (n_1 -1) + ( n_2 +1 )$

df = (8-1)+(8-1)

df = 7 + 7

df = 14

At df = 14 and ∝ = 0.05;

$t _{critical} = 1.760$

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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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

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Degger [83]

Answer:

Inequality of W would be w>7

Step-by-step explanation:

Isolate the variable by dividing each side by factors that do not contain the variable. <em>Hope this helps.</em>

4w-18>10

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2 years ago

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kondaur [170]

Answer:

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Step-by-step explanation:

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Kruka [31]

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