SOLUTION: I need help with this question A midwestern city finds its resident moving to the suburbs. Its population is declining according to the function defined by P(t)=poe-0.04t, wher

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Question 129419: I need help with this question
A midwestern city finds its resident moving to the suburbs. Its population is declining according to the function defined by P(t)=poe-0.04t, where t is time in years and P0 is the population at time t=0. Assume that P0=1,000,000.
I need to find the population at time t=1.
b) how long will it take for the population to decline to 750,000?
c) how long will it take for the population to decline to half the initial number?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
P%28t%29=P%5B0%5De%5E%28-0.04t%29
P%28t%29=%281000000%29e%5E%28-0.04t%29
a) At time t=1,
P%281%29=%281000000%29e%5E%28-0.04%281%29%29 Substitute t=1.
P%281%29=%281000000%29%280.960789%29
P%281%29=960789
At 1 year, the population is now at 960,789.
b)P%28t%29=%281000000%29e%5E%28-0.04t%29=750000
e%5E%28-0.04t%29=0.75
-0.04t=ln%280.75%29 Take the natural log of both sides.
-0.04t=-0.28768
t=7.19
The time to reach 750,000 people would be 7.19 years (approximately 7 years, 2 months).
c)P%28t%29=%281000000%29e%5E%28-0.04t%29=500000
-0.04t=ln%280.50%29 Take the natural log of both sides.
-0.04t=-0.69315
t=17.33
The time to reach 500,000 people would be 17.33 years (approximately 17 years, 4 months).