the population P(t) of a new residential development t years after 2010 is P(t)=8000(1-e^-0.3). What is the population for 2015?

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?

6215 is the right answer. What were the steps without a calculator? Thanks!

To evaluate e^(-.15) without a calculator would be beyond the scope of most of today's college students.

5x-2y=4 m= b=

-x+4y=12 m= b=

To find the population for the year 2015, we need to calculate the value of P(t) when t is equal to 2015 - 2010 = 5 years.

The given population formula is:
P(t) = 8000(1 - e^(-0.3))

To calculate P(5), we substitute t = 5 into the formula:
P(5) = 8000(1 - e^(-0.3))

To compute this, we shall follow the steps below:

Step 1: Calculate the exponent value:
e^(-0.3) ≈ 0.7408

Step 2: Substitute the calculated value into the formula:
P(5) = 8000(1 - 0.7408)
= 8000(0.2592)

Step 3: Multiply the numbers:
P(5) ≈ 2073.6

Therefore, the population for the year 2015 in the new residential development is approximately 2073.6.