the population P(t) of a new residential development t years after 2010 is P(t)=8000(1-e^-0.3t). What is the population for 2015?
* algebra - Reiny, Sunday, December 5, 2010 at 6:19pm
replace t with 5 and evaluate using your calculator
(I got 6215)
I was the population to increase in a new development.
Are you sure your formula is correct?
* algebra - math help, Sunday, December 5, 2010 at 6:52pm
6215 is the right answer. What were the steps without a calculator? Thanks!
you have to evaluate e^(-5) can be done, by this method (1/e)(1/e)(1/e)(1/e)(1/e) That would be fun multiplying without a calculator.
To find the population for 2015 using the given formula P(t) = 8000(1 - e^(-0.3t)), you need to substitute t with the number of years after 2010. In this case, since you are finding the population for 2015, the number of years after 2010 would be 5.
Step 1: Substitute t with 5 in the formula:
P(5) = 8000(1 - e^(-0.3(5)))
Step 2: Simplify the expression inside the parentheses:
P(5) = 8000(1 - e^(-1.5))
Step 3: Calculate e^(-1.5) using the value of e (approximately 2.71828):
P(5) = 8000(1 - 2.71828^(-1.5))
Step 4: Calculate 2.71828^(-1.5) using a calculator:
P(5) = 8000(1 - 0.22313)
Step 5: Simplify the expression inside the parentheses:
P(5) = 8000(0.77687)
Step 6: Multiply the two numbers:
P(5) ≈ 6215
So, the population for 2015 is approximately 6215.