Download Test 2 will emphasize material covered since test 1, and go through

Math 160
Test 2, which will emphasize chapter 3 material, will be on Thursday, 10/20.
At the end of the chapter there is a chapter summary and review (starting on page 233). This is an excellent
source of practice problems (skipping only those that refer to implicit differentiation, which we skipped). You
also have MathXL and class worksheets which you can review. Additionally, here are some more problems:
1. Find y’ for each of the following:
a) 𝑦 = 𝑥 4 − 3𝑥 3 + √2𝑥 + 𝑒
𝑥 3 +2𝑥−7
2.
a.
b.
c.
d.
b) 𝑦 =
𝑥
c) 𝑦 = (𝑥 2 + 1)3𝑥
4
d) 𝑦 = (𝑥 + √𝑥)
e) 𝑦 = 𝑒 −2𝑥+5
f) 𝑦 = (𝑥 2 + 𝑥 + 1)3 (𝑥 4 − 7)
g) y = (ln(x))3
.
$2000 is invested in an account which pays 10% interest.
If the interest is compounded monthly, what will the balance be after 2 years?
If the interest is compounded continuously, what will the balance be after 2 years?
How long will it take to grow to $5000 if the interest is compounded monthly?
How long will it take to grow to $5000 if the interest is compounded continuously?
3. 14 𝐶 has a continuous rate of decay per year of r = -0.000121. A sample initially contains 100mg of
a. Find a formula for the mass of 14 𝐶 which remains after t years.
b. Find the mass of 14 𝐶 remaining after 2000 years.
c. At what rate is the mass decreasing after 2000 years?
14
𝐶:
4. The cost, in $, of producing a certain commodity is C ( x)  500  4 x  .0001x3 . Find C’(100), and carefully
interpret what this value means in this context.
100
5. ACME has found the following demand function for its widgets: 𝑝(𝑥) = 𝑥+1 , where x is the number of
√
widgets to sell, and p is the price, measured in dollars.
a) Find the marginal demand function, p’(x).
b) Show that the marginal demand is always negative – why does this make sense in the context of this
application?
c) Find the revenue as a function of the number of widgets sold, x.
d) Find the marginal revenue function
e) Evaluate R’(400), and interpret this quantity in the context of this application.
6. Find an equation for the tangent line to 𝑦 = ln(𝑥) at x=1.
7. A company’s monthly sales are modeled by 𝑠 = 100000 − 40000𝑒 −.0004𝑥 , where x is that month’s
advertising budget. If x is $2000, and increasing at a rate of $300 per month, at what rate is s increasing?
8. A fast food restaurant can sell 900 hamburgers per day at a price of $4 each, but for each dollar the price is
raised the number of sales goes down 150.
a. Express the demand for this restaurant’s hamburgers as a function of the price.
b. Use the demand function from part (a) to determine at which prices the demand is elastic, at which prices the
demand is inelastic, and at what price the demand has unit elasticity