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07:3640–43. Population growth
A culture of bacteria in a Petri dish has an initial population of 1500 cells and grows at a rate (in cells/day) of N′(t) = 100e^−0.25t. Assume t is measured in days.
a. What is the population after 20 days? After 40 days?
Flow rates in the Spokane River The daily discharge of the Spokane River as it flows through Spokane, Washington, in April and June is modeled by the functions
r1(t) = 0.25t²+37.46t+722.47 (April) and
r2(t) = 0.90t²−69.06t+2053.12 (June), where the discharge is measured in millions of cubic feet per day, and t=0 corresponds to the beginning of the first day of the month (see figure).
a. Determine the total amount of water that flows through Spokane in April (30 days).
Consider the region R in the first quadrant bounded by y=x^1/n and y=x^n, where n>1 is a positive number.
a. Find the volume V(n) of the solid generated when R is revolved about the x-axis. Express your answer in terms of n.
21–30. {Use of Tech} Arc length by calculator
a. Write and simplify the integral that gives the arc length of the following curves on the given interval.
y = x³/3, for −1≤x≤1
A right circular cylinder with height R and radius R has a volume of VC=πR^3 (height = radius).
a. Find the volume of the cone that is inscribed in the cylinder with the same base as the cylinder and height R. Express the volume in terms of VC.
For the given regions R₁ and R₂, complete the following steps.
a. Find the area of region R₁.
R₁ is the region in the first quadrant bounded by the y-axis and the curves y=2x^2 and y=3−x; R₂ is the region in the first quadrant bounded by the x-axis and the curves y=2x^2 and y=3−x(see figure).
