1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dovator [93]
4 years ago
6

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

Mathematics
1 answer:
LUCKY_DIMON [66]4 years ago
3 0
\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
You might be interested in
Solve for x: 4(x-2)+6=2(5x-6)
Katarina [22]

4(x - 2) + 6 = 2(5x - 6)     <em>use distributive property</em>

(4)(x) + (4)(-2) + 6 = (2)(5x) + (2)(-6)

4x - 8 + 6 = 10x - 12

4x - 2 = 10x - 12       <em>add 2 to both sides</em>

4x = 10x - 10       <em>subtract 10 from both sides</em>

-6x = -10      <em>divide both sides by (-6)</em>

x = 10/6

<h3>x = 5/3</h3>
8 0
3 years ago
Which of the following graphs of exponential functions corresponds to a geometric sequence with a first term of 4 and a ratio of
ser-zykov [4K]

Answer: graph E.


A geometric sequence can be written as:

a_{n} = a_{1} \cdot r^{(n - 1)}

where:

a₁ = first term = 4

r = ratio = 0.5


Substituting the numbers, we have:

a_{n} = 4 \cdot (\frac{1}{2})^{n-1}

or else

f(x) = 4 \cdot (\frac{1}{2})^{x - 1}


This is an exponential function with base less than 1. Therefore, we can exclude graph C (which depicts a linear function), and graphs A and D (which depict an exponential function with base greater than 1).


In order to choose between graph B and E, let's evaluate the function in two different points:

f(1) = 4 \cdot (\frac{1}{2})^{1 - 1} = 4

f(2) = 4 \cdot (\frac{1}{2})^{2 - 1} = 4 \cdot \frac{1}{2} = 2


Therefore, we need to look for the graph passing through the points (1, 4) and (2, 2). That is graph E.




3 0
3 years ago
Read 2 more answers
Josie selected a number n. She divided n by 2 and then subtracted 0.5 from the result. She took half of that result and then sub
ycow [4]
Your answer is N= Forty three

8 0
3 years ago
Read 2 more answers
There are 20 boys and 20 girls in a classroom.
Ede4ka [16]

Answer:20

Step-by-step explanation:

7 0
3 years ago
Directions: Simplify the following expressions using the imaginary number.
drek231 [11]

Answer:

1  i(sqrt5)

2  7i

3  -9i

4  -64i

5  -5i(sqrt2)

6  -4i(sqrt3)

7  10i(sqrt3)

8  2i(sqrt2)

9  3i(sqrt7)

10  -30i(sqrt2)

Step-by-step explanation:

i is the square root of (-1). We can simplify each one as such.

5 0
2 years ago
Other questions:
  • SOMEONE PLEASE HELP ALL THE QUESTIONS R ATTACHED AS WELL AS THE ANSWERS!!!!!!!!!!!!!!
    13·1 answer
  • Assume that X is normally distributed with a mean of 20 and a standard deviation of 2. Determine the following. (a) P(X 24) (b)
    14·1 answer
  • Parents wish to have $160,000 available for a​ child's education. If the child is now
    13·1 answer
  • Plz help me ASAP I will give Brainliest if right. What is the probability that he gets a number less than 4 or A multiple of 4?
    11·1 answer
  • Dana needs 300 pickets for her colorful picket fence. She wants equal amounts of each of her four selected colors. She already h
    12·1 answer
  • Help me solve this thanks!!1 : )
    11·2 answers
  • Pleaseeeeeeee helppppppppppppppppppppppppppppp
    14·1 answer
  • Mr. Rozario bought some oranges and some apples. The ratio of oranges to apples is 2:5. He gave 3/4 to his sister and 34 oranges
    13·1 answer
  • Order of operations <br> 18 ÷ 9 - 4 x 15
    6·2 answers
  • Help! Please i need it badly
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!