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Triss [41]
3 years ago
11

HELP!!! i need it asap, thank you

Mathematics
1 answer:
Step2247 [10]3 years ago
7 0
Answer: H

Step by Step
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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
1. Classify the triangle according to side length and angle measurement.
mezya [45]

Answer:

1. Scalene right

2. Isosceles acute

3. Parallelogram

3 0
3 years ago
Read 2 more answers
PLEase hurry please hURyy plaese hurry
steposvetlana [31]

<h2><u>PLEASE MARK BRAINLIEST!</u></h2>

Answer:

All these answers are correct. I triple - checked!

Step-by-step explanation:

In order from questions asked top - to - bottom:

First question:

  • 23 businesses

Second question:

  • 18 businesses

Third question:

  • 14 businesses

Fourth question:

  • 6 businesses

I hope this helps!

- sincerelynini

6 0
2 years ago
In Ms. Craig’s class, 75% of the students are boys. There are 18 boys in the class. What is the total number of students in Ms.
topjm [15]

Answer:

24

Step-by-step explanation:

75% of x = 18

75/100 * x = 18 (x =  total number of students)

solving

x = 24

total number of students = 24

Checking:

75/100 * 24 = 18

5 0
3 years ago
6x+4y=42 -3x+3y=-6 by elimination
creativ13 [48]

Answer:

x=5, y=2

Step-by-step explanation:

To solve this system, we need to find x and y. First, let's find x. In the first equation (6x+4y=42), subtract 4y on both sides to isolate 6x. This will result in 6x=42-4y. Divide by 6 on both sides to isolate x and get x=7-\frac{2}{3}y. Now we know what x equals. Go to the second equation ad plug this into it. So instead of -3x+3y=-6, you'll have -3(7-\frac{2}{3}y)+3y=-6. Use the distributive property to get -21+2y+3y=-6. Add 2y and 3y to get -21+5y=-6. Add 21 to both sides to isolate 5y and get 5y=15. Divide by 5 on both sides to isolate y and get y=3. Now that we know that y=3, we can plug this back into the equation that was bolded above so that we can find x, so we'll have x=7-\frac{2}{3}(3) since y=3, and we'll get x=7-\frac{6}{3}, or x=7-2, or x=5.

x=5

y=2

6 0
3 years ago
Read 2 more answers
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