The population of a Midwestern city decays exponentially. If the population decreased from 900,000 to 800,000 from 2003 to 2005, what will be the population in 2008?
Please help I got 670,422 and the computer marked it wrong i then tried rounding it to 671000 but it was still wrong! Please help me THank you
Both Scott and I did this for you here , and we both got the same answer
http://www.jiskha.com/display.cgi?id=1489120237
(900,000 - 800,000)/2 = 50,000/yr.
P = 800,000 - (50.000/yr. * 3yrs) =
800,000 - 150,000 = 650,000.
It said exponentially. You made it a linear decay.
Yes,thanks!
To find the population in 2008, we first need to determine the growth rate. Since the population decays exponentially, we can use the formula:
P(t) = P₀ * e^(kt)
Where:
P(t) represents the population at time t
P₀ represents the initial population
e is the base of the natural logarithm (approximately 2.71828)
k is the decay rate
t represents the time elapsed
Given that the population decreased from 900,000 to 800,000 from 2003 to 2005, we can find k using the following steps:
1. Find the decay factor, which is the ratio of the final population to the initial population:
Decay factor = P₁ / P₀ = 800,000 / 900,000
2. Take the natural logarithm (ln) of the decay factor:
ln(decay factor) = ln(800,000 / 900,000)
Now, let's calculate this value to find k:
decay factor = 800,000 / 900,000 ≈ 0.88889
ln(decay factor) ≈ ln(0.88889) ≈ -0.11831
Next, we can substitute this value of k into the exponential decay formula:
P(t) = P₀ * e^(kt)
We know that the population P(t) in 2005 was 800,000, so we can use this value to solve for P₀:
800,000 = P₀ * e^(-0.11831 * 2)
Simplifying the equation further:
800,000 = P₀ * e^(-0.23662)
Finally, we can use this equation to find the population P(t) in 2008 by setting t = 2005 - 2008 = -3:
P(-3) = P₀ * e^(-0.11831 * -3)
Calculating e^(-0.11831 * -3):
e^(-0.11831 * -3) ≈ e^0.35493
Multiplying this exponential factor by 800,000:
P(-3) ≈ 800,000 * e^0.35493
Now, you can use a calculator to find the approximate value of P(-3) and determine the population in 2008.