Related Rates - AP Calculus

Calculator: The rate of change of the altitude of a hot-air balloon is give by r(t) = t³-4t²+6 for 0≤t≤8. Which of the following expressions gives the change in altitude of the balloon during the time the altitude is deceasing?

• A
• B
• C
• D

Non-Calculator: The rate of change of the volume, V, of water in a tank with respect to time, t, is directly proportional to the square root of the volume. Which of the following is a differential equation that describes this relationship?

• V(t) = k√t
• dV/dt = k√t
• dV/dt = k/√V
• dV/dt = k√V

Non-Calculator: Find the instantaneous rate of
f(t) = (2t³-3t+4) √(t²+3t+4)
at t=0.

• -3
• -3/4
• -4
• -5/4

Calculator: The amount of money in a bank account is increasing at a rate of 
R(t)=1000e^(0.06t)
dollars per year, where t is measured in years. If t=0 corresponds to the year 2005, then what is the approximate total amount of increase from 2005 to 2007.

• $18,350
• $32,560
• $21,250
• $16,250

Calculator: At what approximate rate (in cubic meters per minute) is the volume of a sphere changing at the instant when the surface area is 5 square meters and the radius is increasing at the rate of 1/3 meters per minute?

• 1.667
• 5.271
• 1.080
• 2.714

Calculator: What is the approximate instantaneous rate of change of the function at t=π/7?

• -.9009
• -7.207
• 3.473
• -1.030

Non-Calculator: What is the instantaneous rate of change at x=2 of the function f given by 
f(x) = (x²-2)/(x-1) ?

• -2
• 1/6
• 1/2
• 2

Calculator: Population y grows according to the equation
dy/dt=ky
where k is a constant and t is measured in years. If the population doubles every 10 years, the the value of k is

• 0.069
• 0.200
• 0.301
• 3.322

Calculator: What is the average rate of change of
f(x)=(e^1/x)/x²
in the interval -4≤x≤-1?

• 0.106
• 0.137
• 0.319
• 1.233

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Calculator: Shampoo drips from a crack in the side of a bottle at a rate modeled by 
Y(t) = t / √(1+t^3/2)
where Y(t) is in ounces per minute. If there are 32 ounces in the bottle t=0, how many ounces are left the bottle after 5 minutes?

• 5.063 ounces
• 24.355 ounces
• 26.937 ounces
• The bottle will be empty before 6 minutes has elapsed