For problems 1 10 find all the solutions to the given
equation. If there is no solution to the
equation clearly explain why.
Compound Interest.
If we put P dollars into an account
that earns interest at a rate of r
(written as a decimal as opposed to the standard percent) for t years then,
- if interest is compounded m times per year we will have,
dollars after t years.
- if interest is compounded
continuously we will have,
dollars after t years.
13. We have $10,000 to invest for 44 months. How much money will we have if we put the
money into an account that has an annual interest rate of 5.5% and interest is
compounded
(a) quarterly (b) monthly (c) continuously
[Solution]
14. We are starting with $5000 and we’re going to put it
into an account that earns an annual interest rate of 12%. How long should we leave the money in the
account in order to double our money if interest is compounded
(a) quarterly (b) monthly (c) continuously
[Solution]
Exponential
Growth/Decay. Many quantities in the
world can be modeled (at least for a short time) by the exponential
growth/decay equation.
If k is positive
then we will get exponential growth and if k
is negative we will get exponential decay.
15. A population of bacteria initially has 250 present and
in 5 days there will be 1600 bacteria present.
(a) Determine the
exponential growth equation for this population.
(b) How long will
it take for the population to grow from its initial population of 250 to a population
of 2000?
[Solution]
16. We initially have 100 grams of a radioactive element and
in 1250 years there will be 80 grams left.
(a) Determine the
exponential decay equation for this element.
(b) How long will it take for half of the
element to decay?
(c) How long will
it take until there is only 1 gram of the element left?
[Solution]
Problem Pane