In 2012, the population of a city was 6.63 million. The exponential growth rate was 3.01% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 11 million?
d) Find the doubling time.
Answers
Answer:
So first we need to determine what the exponential growth function would look like. Exponential growth functions look like [tex]P(t) = P_0*e^{r*t}[/tex] and in our case [tex]P_0[/tex] would be the initial population which is 6.63 million. R is the next variable that we need to fill out which is the rate of change which in our case is 3.01% or 0.0301.
This is how our function should look now [tex]P(t)=6.63*e^{0.0301*t}[/tex]
Moving onto part b, we need to estimate the population of the city in 2018 which 6 years from 2012 and we plug that into t and solve.
[tex]P(t) = 6.63 * e^{0.0301*6}[/tex]
[tex]P(t) = 6.63*e^{0.1806}[/tex]
[tex]P(t) = 6.63 *1.1979[/tex]
[tex]P(t) = 7.9423\ million[/tex]
Moving onto part c, we need to find when the population of the city will be 11 million which will be done by setting P(t) to 11 million and solving for t.
[tex]11 = 6.63*e^{0.0301*t}[/tex]
[tex]\frac{11}{6.63} = \frac{6.63*e^{0.0301*t}}{6.63}[/tex]
[tex]1.659=e^{0.0301*t}[/tex]
[tex]ln(1.659)=ln(e^{0.0301*t})[/tex]
[tex]\frac{0.506}{0.0301}=\frac{0.0301*t}{0.0301}[/tex]
[tex]16.818\ years = t[/tex]
Moving onto part d, we need to find the doubling time. This will be similar to the previous part but we will be finding the time it takes to double our population. So instead of putting 11 million for P(t) we put 6.63 * 2 in there which is 13.26.
[tex]13.26 = 6.63*e^{0.0301*t}[/tex]
[tex]\frac{13.26}{6.63} = \frac{6.63*e^{0.0301*t}}{6.63}[/tex]
[tex]2=e^{0.0301*t}[/tex]
[tex]ln(2)=ln(e^{0.0301*t})[/tex]
[tex]\frac{0.693}{0.0301}=\frac{0.0301*t}{0.0301}[/tex]
[tex]23.028\ years = t[/tex]
Hope this helps! Let me know if you have any questions
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What are Caleb's bank fees?The question is incomplete so I will use a similar question to answer it.
Caleb's fees at Neobank would be:
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= $11
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= $15.70
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Answers
Answer:
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Answer:
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Answers
Answer:
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x² + y² = 14
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Answers
Step-by-step explanation:
83 +(25)/5 >32 + 42
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Step-by-step explanation:
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Answers
The formula of a cylinder is 2πr (r+h)
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EFG = 98°
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Minor arc EG = 196°
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Answers
Answer:
126 mi²
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First Run
Second Run Total
Children 122 146 268
Adults 183 219 402
Total 305 365 670
Based on the data in the table, what is the value of P(Adult|Second run) rounded to the nearest thousandth?
Answers
The two-way table is an illustration of probability, and the value of P(Adult|Second run) is 0.600
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This means:
The probability that an Adult is selected given that the adult runs the second run
The formula to solve this is:
P(Adult|Second run) = n(Adult and Second run)/n(Second run)
From the table, we have:
n(Adult and Second run) = 219
n(Second run) = 365
So, we have:
P(Adult|Second run) = 219/365
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P(Adult|Second run) = 0.600
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Answer:
The value of P rounded to the nearest thousandth would be 0.6
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In a soccer league with four teams, each team played four games with every other team. Each team received 3 points for a win, 1 point for a tie, and no points for a loss. After all the games, the point tallies were as follows: Team A won 22 points, team B won 19 points, team C won 14 points, and team D won 12 points. How many games ended in a tie?
Answers
The number of game that ended in a tie are= 67
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Answers
Answer:
[tex]A = 9\pi[/tex]
Step-by-step explanation:
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Plug in 6 for the radius:
[tex]A = \frac{3}{4} \pi (6)^{2}[/tex]
Simplify:
[tex]A = \frac{3}{4} \pi (36)[/tex]
Simplify further:
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Step-by-step explanation:
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Solution:
(a)
1) centimeters
2) inches
(b) Solution: Randomly pick 50 students from the 9th grade and measure their heights.
2) A box contains 9 red and 2 blue marbles and 3 yellow marbles. If you select oneat
random from the box, determine:
a) The probability the marble is red.
b) The odds in favor of selecting a red marble.
c) The probability the marble is blue.
d) The odds against selectinp a hlue marble
Answers
Answer:
red is more in value unlike the rest
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Answers
Answer:
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Answers
Answer: p = 9h
Step-by-step explanation:
If she makes 9 dollars of every hour of work, this will be a linear equation. We will write it as the following:
p = 9h
Answer:
9h/p
Step-by-step explanation:
9 x # of hours = total pay
$9 is the dollars for each hour, so you multiply that by how many hours Maria works. You will get the total pay.
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Answers
Answer:
275.46
Step-by-step explanation:
She has $325.31
she writes a check for $24.85
she withdrew $40
and deposited $15
so do 325.31-24.85-40+15
and that equals
275.46
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cos 32° = sin
Answers
[tex]\cos32^{\circ} \\\\=\sin(90-32)^\circ~~~~~~~~~~~~~~;[\cos \theta = \sin(90- \theta)]\\\\=\sin 58^{\circ}[/tex]
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Step-by-step explanation:
Answer:
1. minerals = B inorganic elements
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Step-by-step explanation: