The function fx is decreasing and concave up on the interval ab The function fx

# The function fx is decreasing and concave up on the

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The function f(x) is decreasing and concave up on the interval [a,b]. The function f(x) is increasing and concave down on the interval [a,b].

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Correct! The function is decreasing and linear on the interval [a,b]. The function f(x) is increasing and concave up on the interval [a,b]. The function f(x) is decreasing and concave down on the interval [a,b]. The function f(x) f(x) is decreasing and linear on the interval [a,b] [a,b]. Question 10 1.67 / 1.67 pts Suppose a firm that produces pints of gourmet ice cream has monthly fixed costs of \$12,000. The variable costs come to \$1.50 per pint produced. (for up to 40,000 pints/month) and the firm sells each pint of ice cream for \$3. Find the firm's profit function. P(x)=x−12000 P(x)=x−12000 Correct! P(x)=1.5x−12000 P(x)=1.5x−12000 P(x)=1.5x 2 +12000 P(x)=1.5x2+12000 P(x)=3x 2 −1.5x−120000 P(x)=3x2−1.5x−120000
P(x)=1.5x 2 −3x−12000 P(x)=1.5x2−3x−12000 The revenue function R(x)=3x R(x)=3x. The cost function C(x)=1.5x+12000 C(x)=1.5x+12000 P(x)=R(x)−C(x)=3x−(1.5x+12000)=1.5x−12000 P(x)=R(x) −C(x)=3x−(1.5x+12000)=1.5x−12000 Question 11 0 / 1.67 pts Simplify the expression: (xy b2 ) b2 (xy−b2)b2 You Answered x b2 y xb2y x b 2y b xb2yb x b2 xb2 b2 xy b2xy Correct Answer x b2 y b24 xb2yb24 (xy b2 ) b2 =x b2 y −( b2 )( b2 ) =x b2 y b24 =x b2 y b24 (xy−b2)b2=xb2y−(b2) (b2)=xb2y−b24=xb2yb24 Question 12

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1.66 / 1.66 pts The following formula describes the quantity Q of a substance in milligrams (mg) as a function of time t, in hours. Q=30+15t. Q=30+15t. Choose the correct statement below. When t=0, Q=30mg. Q is decreasing exponentially at 30% per hour. Correct! When t=0, Q=30mg. Q is increasing linearly at 15 mg per hour. When t=0, Q=30mg. Q is increasing exponentially at 15% per hour. When t=0, Q=0mg. Q is increasing exponentially at 15% per hour. When t=0, Q=15mg. Q is decreasing linearly at 30mg per hour. When t=0 t=0, Q=30+15⋅0=30 Q=30+15 0=30 mg. Q Q is increasing linearly, at 15 mg per hour. Question 13 1.67 / 1.67 pts A quantity P is a exponential function of time t, that is P=P 0 a t , P=P0at, where a is a positive constant and P 0 P0 is the quantity at t=0. Suppose that P=100 when t=1,P=75 when t=4 P=100 when t=1,P=75 when t=4
Use this information to find a and P 0 P0 and state the rate of exponential growth or decay. a=1.09, P 0 =110 P0=110 , exponential growth at a rate of 9%. a=1.05, P 0 =125 P0=125 , exponential growth at a rate of 5%. a=0.86, P 0 =137 P0=137 , exponential decay at a rate of 14%. Correct! a=0.91, P 0 =110 P0=110 , exponential decay at a rate of 9%. a=0.75, P 0 =133 P0=133 , exponential decay at a rate of 25%. We have two equations and two unknowns. We can eliminate P 0 P0 if we first solve each equation for P 0 P0. This first step gives us two equations for P 0 P0. P 0 = 100a ,P 0 = 75a 4 P0=100a,P0=75a4 We have two expressions that both equal P 0 P0, so we can set them equal to each other, and then solve for a a:

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Use a=0.91 a=0.91 in either above equation to find P 0 P0. You should get the same answer either way so you can use both as a check. P 0 = 1000.91 =110 P0=1000.91=110 Question 14 1.67 / 1.67 pts Suppose a firm has a linear profit function P(x) = 5x-3000. This function has one x- intercept. Interpret the meaning of the x-intercept in economic terms.

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