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Math 125 Pre- Calculus Name:___________________________
Spring 2013, Kenny Shah (Chapter 4)
In-Class Assignment # 4(4.1 – 4.5)
1. An investment decreases by 5% per year for 4 years. By what total percent does it decrease?
2. The amount (in milligrams) of a drug in the body t hours after taking a pill is given by
.
(a)
What is the initial dose given?
(b)
What percent of the drug leaves the body each hour?
(c)
What is the amount of drug left after 10 hours?
(d)
After how many hours is there less than 1 milligram left in the body?
3. A population has size 5000 at time t = 0, with t in years.
(a)
If the population decreases by 100 people per year, find a formula for the population, P, at time t.
(b)
If the population decreases by 8% per year, find a formula for the population, P, at time t.
4. find a formula for the exponential function
5. Assume the equations for , , , and can all be written in the form .
Which function has the largest value for a?
Which two functions have the same value for a?
Which function has the smallest value for b?
Which function has the largest value for b?
6. The number of asthma sufferers in the world was about 84 million in 1990 and 300 million in 2009. Let N represent the number of asthma sufferers (in millions) worldwide t years after 1990.
(a)
Write N as a linear function of t. What is the slope? What does it tell you about asthma sufferers?
(b)
Write N as an exponential function of t. What is the growth factor? What does it tell you about asthma sufferers?
7. Assume that all important features are shown in the graph of . Estimate
a.
b.
8. A bank pays interest at the nominal rate of 1.3% per year. What is the effective annual rate if compounding is:
(a)
Annual
(b)
Monthly
9. Suppose $1000 is deposited into an account paying interest at a nominal rate of 8% per year. Find the balance three years later if the interest is compounded
(a)
Monthly
(b) Find the nominal and effective rate of the investment.
(c) What does the effective rate mean to you in terms of the application problem.
10. One bank pays 5% interest compounded annually and another bank pays 5% interest compounded continuously. Given a deposit of $10000, what is the difference in the balance between the two banks in 8 years?
11. Rank the following three bank deposit options from best to worst.
•
Bank A: compounded daily
•
Bank B: compounded monthly
•
Bank C: compounded continuously
12. A population grows from its initial level of 22000 at a continuous growth rate of 7.1% per year.
(a)
Find a formula for P=f(t), the population in year t.
(b)
By what percent does the population increase each year?
