Prof. S. Brick Math 120
Fall ’02 Applied Calculus; Final Exam Review section 52
1. You leave home for calculus, driving slowly when you realize that you forgot your
brownies. You turn around and drive faster and faster until a cop pulls you over. Luckily,
you use Calculus to avoid a ticket. But you get so depressed from it that you decide to
spend the day in bed. Sketch a graph of the distance you are from class as a function of
time.
2. You have a budget for textbooks and social events of $1400. Textbooks cost $100 each.
A night out costs $70. Find and graph the equation of your budget constraint. Shade in
the region of living within your means. What do points on the axes represent ?
3. The half-life of Mobilium is 6.6 hours. How long before 16 grams decays into 11 grams
4. Find Z4
2
x3dx
5. Let f(v) be the fuel efficiency of a car in mpg that is driven at an average speed vmph.
What are the units of f0(v) ? What would f0(70) = −.5 tell you ?
6. Sketch the graph of a function defined for whose first derivative is always positive but
whose second derivative starts out positive and changes it sign twice.
7. Suppose M R(100) = 95 and M C (100) = 72. Estimate what happens to the profit if
the production is changed to a level of q= 104.
8 A ball is tossed up in the air. A total of 6 seconds elapses from the moment it is tossed
until it hits the ground. Sketch a graph of the velocity as aa function of time for 0 ≤t≤6.
9 Find the present value of an income stream of one million dollars a year over 5 years
assuming an annual interest rate of 10%.
10. Find the equation of the line tangent to y=√x2+ 7 at x= 3. On a single graph
sketch both the original function and the tangent line.
11. Using the left-hand rule with 4 evenly-spaced rectangles set up (but do not compute)
the Riemann sum for R2
1ln(x)dx. Sketch a graph showing the rectangles.
12. Suppose f(5) = 119.1 and f(25) = 31.7. Find two possible values for f(45), one if f
is linear and the other if fis exponential. Explain your calculation.
13. A population of rabbits are introduced to an island. Suppose initially there are 3000
rabbits and that the population grows at an annual rate of 20.25%. Using a non-logistic
exponential model, find the time it takes for the population to reach 100,000. Why would
a logistic model be better to use ?
