The population of a town is modeled by the equation P=3485e0.12t, where “P” represents the population as of the year 2000.
According to the model, what will the population of the town be in 2010?
In approximately what year will the population reach 50,000 people?
Must answer and show appropriate work for both questions here.
Part A: 11,571 people in 2010
Part B: approx. 22 years
Part A: 38,416 people in 2010
Part B: approx. 13 years
Part A: 11,571 people in 2010;
Part B: approx. 13 years
Part A: 38,416 people in 2010;
Part B: approx. 22 years
P=3485 e^ .12t this is the equation sorry typo
It would help if you would proofread your work before you post it.
What is "P=3485e0.12t,"?
Whats the correct answer? i think it is A.
Well, let's find the population of the town in 2010 using the given model. Plugging in t = 10 (since 2010 is ten years after 2000), we get:
P = 3485e^(0.12*10) = 3485e^1.2 ≈ 11,571
So the population of the town in 2010 would be approximately 11,571 people.
To determine when the population will reach 50,000 people, we need to solve the equation for t. Plugging in P = 50,000, we have:
50,000 = 3485e^(0.12t)
Dividing both sides by 3485:
e^(0.12t) = 14.35
Taking the natural logarithm of both sides:
0.12t ≈ ln(14.35)
Solving for t:
t ≈ ln(14.35) / 0.12 ≈ 22
So the population of the town will reach 50,000 people in approximately 22 years.
In order to determine the population of the town in 2010 using the given equation P=3485e^0.12t, we need to substitute the value of t with the corresponding year.
For Part A:
Substituting t = 2010 - 2000 = 10 into the equation, we get:
P = 3485e^(0.12 * 10) = 3485e^1.2 ≈ 11571
Therefore, the population of the town in 2010 is approximately 11,571 people.
To determine the year in which the population reaches 50,000 people, we can rearrange the equation and solve for t.
For Part B:
50,000 = 3485e^(0.12t)
Dividing both sides by 3485, we get:
e^(0.12t) = 50,000/3485 ≈ 14.355
Take the natural logarithm (ln) of both sides to isolate the exponent:
ln(e^(0.12t)) = ln(14.355)
0.12t = ln(14.355)
Divide both sides by 0.12 to solve for t:
t = ln(14.355)/0.12 ≈ 22
Therefore, the population of the town will reach 50,000 people in approximately 22 years.
P=3485e^0.12t
let 2000 correspond with t = 0, then for 2010 , t = 10
sub t = 10 into the equation and calculate
when is P = 5000?
5000 = 3485 e^(.12t)
take ln of both sides
ln 5000 = ln 3485 + .12t ln e
.12t = ln5000 - ln3485 = .36096...
t = 3.008..
which would correspond with 2003