**Problem : **
Which investment earns more interest: $10,000 at 6.2% interest compounded
quarterly (4 times per year) for twenty years, or $10,000 at 7.5% interest
compounded continuously for 15 years?

$10,000 at 6.2% interest compounded quarterly (4 times per year) for twenty
years:

*A*(*t*) = 10, 000(1 + )^{80} 34, 229 dollars.
$10,000 at 7.5% interest compounded continuously for 15 years:

*A*(*t*) = 10, 000*e*^{1.125} 30, 802. The first investment earns more interest.

**Problem : **
How soon will an investment double its value if it is invested at 5%
compounded monthly?

In about

13.89 years the value of the investment will have doubled.

**Problem : **
A city's population grows at the constant relative rate of 6%. If the
original population is 10, 000, how many people are there after ten years?

*P*(*t*) = 10, 000*e*^{.06t}.10, 000*e*^{.60} 18, 221 people.

**Problem : **
The population of a bacteria culture exponentially grows from 2,000 to 20,000 in
six hours. What is the constant relative rate of growth?

*P*(*t*) = *P*(0)*e*^{kt}.20, 000 = 2, 000*e*^{6k}.*e*^{6k} = 10.*k* = .3838. The growth rate is approximately 38.38%.