Choose the correct rule for the graph shown. Please Help 30POINTS

A model for the population in a small community after t years is given by P(t)=P0e^kt.

LUCKY_DIMON [66]

$\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\\
\end{cases}$

a)

so, if the population doubled in 5 years, that means t = 5. So say, if we use an amount for "i" or P in your case, to be 1, then after 5 years it'd be 2, and thus i = 1 and A = 2, let's find "r" or "k" in your equation.

$\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &2\\
I=\textit{initial amount}\to &1\\
r=rate\\
t=\textit{elapsed time}\to &5\\
\end{cases}
\\\\\\
2=1\cdot e^{5r}\implies 2=e^{5r}\implies ln(2)=ln(e^{5r})\implies ln(2)=5r
\\\\\\
\boxed{\cfrac{ln(2)}{5}=r}\qquad therefore\qquad \boxed{A=e^{\frac{ln(2)}{5}\cdot t}} \\\\\\
\textit{how long to tripling?}\quad 
\begin{cases}
A=3\\
I=1
\end{cases}\implies 3=1\cdot e^{\frac{ln(2)}{5}\cdot t}$

$\bf 3=e^{\frac{ln(2)}{5}\cdot t}\implies ln(3)=ln\left( e^{\frac{ln(2)}{5}\cdot t} \right)\implies ln(3)=\cfrac{ln(2)}{5} t
\\\\\\
\cfrac{5ln(3)}{ln(2)}=t\implies 7.9\approx t$

b)

A = 10,000, t = 3

$\bf \begin{cases}
A=10000\\
t=3
\end{cases}\implies 10000=Ie^{\frac{ln(2)}{5}\cdot 3}\implies \cfrac{10000}{e^{\frac{3ln(2)}{5}}}=I
\\\\\\
6597.53955 \approx I$

3 0

3 years ago

The annual salaries of all employees at a financial company are normally distributed with a mean of $34,000 and a standard devia

lora16 [44]

z-score of a company is 5.

What is z- test?

A z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large.

The annual salaries of all employees at a financial company are normally distributed with a mean of $34,000 and a standard deviation of $4,000.

Now, using z- score

z= (x- $\mu$ )/ $\sigma$

z= 54000- 34000/ 4000

z= 20000/4000

z=5.

Hence, z-score of a company is 5.

Learn more about this concept here:

brainly.com/question/1546834

#SPJ1

8 0

2 years ago

What number should be added to both sides of the equation to complete the square? x^2 â 10x = 7?

Harman [31]

You should add 25 because you should always add the square of the p value (which is equal to half of the b value, which makes the p value 5).
Basically, the p value should be half of b and the square root of c.

5 0

3 years ago

Chen rode his skateboard 3/3/4 miles in 34 of an hour.

netineya [11]

Answer:

5 miles per hour

Step-by-step explanation:

3¾ ÷ ¾ =

15/4 ÷ ¾ =

15/4 x 4/3 =

15/3 = 5

6 0

2 years ago

Consider the ratio 3:5. Can you create an equivalent ratio by adding the same number to each quantity in the ratio? Explain

iragen [17]

Yes because the unit rate would be 1:2 and that's the rate of change in which 3:5 has.
HOPE IT HELPS!!

4 0

2 years ago

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