Section 3.6
1.
Let f (t) = t 2 .
a. Find the relative rate of change of this function.
b. Evaluate the relative rate of change when t = 1.
c. Evaluate the relative rate of change when t = 10.
2.
Let f (t)  et
2
a. Find the relative rate of change of this function.
b. Evaluate the relative rate of change when t = 10.
3. Let f (t) = 25 (t – 1).
a. Find the relative rate of change of this function.
b. Evaluate the relative rate of change when t = 6.
4. ECONOMICS: National Debt. If the national debt of a country (in trillions of dollars) t years from now is given by
the following function, find the relative rate of change of the debt 10 years from now.
N (t) = 0.5 + 1.1 e 0.01t
5. GENERAL: Population. The population (in millions) of a city t years from now is given by
P (t) = 4 + 1.3 e 0.04t .
a. Find the relative rate of change of the population 8 years from now.
b. Will the relative rate of change ever reach 1.5%?
6. For the demand function, D (p) = 200 – 5p;
a. Find the elasticity of demand E (p)
b. Determine whether the demand is elastic, inelastic, or unit elastic at a price of p = 10.
7. For the demand function, D (p) = 300 – p 2;
a. Find the elasticity of demand E (p)
b. Determine whether the demand is elastic, inelastic, or unit elastic at a price of p = 10.
8. For the demand function, D (p) = 300/p;
a. Find the elasticity of demand E (p)
b. Determine whether the demand is elastic, inelastic, or unit elastic at a price of p = 4.
9. For the demand function, D (p) = 100/p 2 ;
a. Find the elasticity of demand E (p)
b. Determine whether the demand is elastic, inelastic, or unit elastic at a price of p = 10.
10. AUTOMOBILE SALES - An AUTOMOBILE DEALER IS SELLING CARS AT A PRICE OF $12,000. The demand function is
D(P) = 2(15 – 0.001P)2, where p is the price of a car. Should the dealer raise or lower the price to increase the
revenue?
11. CITY BUS REVENUES – The manager of a city bus line estimates the demand function to be D (p) = 150,000 (1.75
– p) ½, where p is the fare in dollars. The bus line currently charges a fare of $1.25, and it plans to raise the fare
to increase its revenues. Will the strategy succeed?
12. OIL PRICES – A European oil-producing country estimates that the demand for its oil (in millions of barrels per
day) is D (p) = 3.5 e – 0.06p, where p is the price of a barrel of oil. To raise its revenues, should it raise or lower its
price from its current level of $120 per barrel?