HW #77 Answers

HW #77 Answers:
1. a. y = 22,000(.875)t
b. ≈ $14738
2. a. y = 110(1.04)t
b. y = 525(1.05)t
c. y = 250(.93)t
3. y = 30000(1.05)t
b. ≈ $344,022
4. a. y = 15000(.75)t
b. Sam is right because using
John's formula the value would be
$8437.50 after 2 years.
5. a. y =5000(1.024)t
b. ≈ $6338.25
Mixed Review:
1. Domain: All Reals
Range: (-∞,5]
2. x =
Aim #78: How do we determine the number of years it will take an
exponential function to reach a value?
Do Now: If $400 is invested into a bank account that earns 3.2%
interest annually, how much will there be in the account after 15
years?
1. If a person takes a given dosage (d) of a particular medication, then the
formula f(t) = d (0.8)t represents the concentration of the medication in the
bloodstream t hours later. If Charlotte takes 200 mg of the medication at
6:00 a.m., how much remains in her bloodstream at 10:00 a.m.?
How long does it take for the concentration to drop below 1 mg?
2. When you breathe normally, about 12% of the air in your lungs is replaced
with each breath. Write an explicit formula for the sequence that models the
amount of the original air left in your lungs, given that the initial volume of
air is 500 mL. Use your model to determinehow much of the original 500 mL
remains after 50 breaths.
After how many breaths will 200 mL remain?
A tennis ball is dropped from a height of 12 feet. Each time the ball
bounces back to 80% of the height from which it fell.
3.
a. Write a formula that models the height of the ball after b bounces.
b. What is the height of the ball after 3 bounces?
c. Graph the points (b, f(b)) for integer values of 0 ≤ b ≤ 9 . Label
and scale both axes.
d. When will the height of the
ball fall below 3 feet?
4. The Booster Club raised $30,000 for a sports fund. No more
money will be placed into the fund. Each year the fund will decrease
by 4 ½%. Determine the amount of money, to the nearest cent, that
will be left in the sports fund after 4 years.
After how many years will the fund drop below $10,000?
5. A pool holds a maximum of 20,500 gallons of water. It evaporates
at a rate of 0.5% per hour. The pool currently contains 19,000 gallons
of water.
a. Write an exponential function w(t) to express the amount of water
remaining in the pool after time t where t is the number of hours
after the pool reached 19,000 gallons.
b. At the same time, a hose is turned on to refill the pool at a net
rate of 300 gallons per hour. Write a function p(t) where t is the
time in hours the hose is running to express the amount of
water that is pumped into the pool.
c. Find C(t) = p(t) + w(t). What does this new function represent?
d. Use the graph or table of values for C(t) to determine after how
many hours the pool will reach its maximum capacity.
6. A piece of machinery that costs $8,000 depreciates each year by
an amount equal to 1/10 of its value of the beginning of the year. To
the nearest dollar, how much will the machine be worth at the end of
the 5th year?
When will the value be less than $1000?