For problems 1 14 find all the solutions to the given
equation. If there is no solution to the
equation clearly explain why.
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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.
18. We have $2,500 to invest and 80 months. How much money will we have if we put the
money into an account that has an annual interest rate of 9% and interest is
compounded
(a) quarterly (b) monthly (c) continuously
19. We are starting with $60,000 and we’re going to put it into
an account that earns an annual interest rate of 7.5%. How long will it take for the money in the
account to reach $100,000 if the interest is compounded
(a) quarterly (b) monthly (c) continuously
20. Suppose that we put some money in an account that has an
annual interest rate of 10.25%. How long
will it take to triple our money if the interest is compounded
(a) twice a year (b) 8 times a year (c) continuously
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.
21. A population of bacteria initially has 90,000 present
and in 2 weeks there will be 200,000 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 90,000
to a
population of 150,000?
22. We initially have 2 kg grams of some radioactive element
and in 7250 years there will be 1.5 kg 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 250 grams of the element left?
23. For a particular radioactive element the value of k in the exponential decay equation is
given by .
(a) How long will
it take for a quarter of the element to decay?
(b) How long will
it take for half of the element to decay?
(c) How long will
it take 90% of the element to decay?