The population of a city (in millions of people) is modled by p(t_ = 3e^t/5 with t=0 representing the year 2000.

a. When(to the nearest year) will the population be 100 million? when will it be a billion
b. At what rate is the population increasing in 2005? IN 2010? Indicate units.
c. Use the 2nd derivative to justify why p'(10)p'(5)

Question

The population of a city (in millions of people) is modled by p(t_ = 3e^t/5 with t=0 representing the year 2000.

a.  When(to the nearest year) will the population be 100 million?  when will it be a billion
b.  At what rate is the population increasing in 2005?  IN 2010?  Indicate units.
c.  Use the 2nd derivative to justify why p'(10)>p'(5)

campbell_st · Answer

quick question 

is the model 

1.

$$P(t) = 3e^{\frac{t}{5}}$$

or 

2. 

$$P(t) = \frac{3e^t}{5}$$

anonymous · Answer

1

anonymous · Answer

a. P(t) is equal to 100 in the first part.
100 = 3e^(t/5)

We're solving for t. 
100/3 = e^(t/5)

Take natural log of both sides, which will get rid of the e

log (100/3) = t/5
Multiply both sides by 5
t = 5log(100/3)

Use calculator, and its 7.614, or 2000 + 8, to the nearest years: 2008
Try the second part yourself.

anonymous · Answer

okay but how do you do part c.