Hint Ask yourself how much the profit is at the x intercept The x intercept is

# Hint ask yourself how much the profit is at the x

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Hint: Ask yourself how much the profit is at the x-intercept. The x-intercept is -3000. The firm has fixed costs of \$3000. The x-intercept is 600. This is the firm's marginal profit. The x-intercept is 5. This is the firm's marginal revenue. Correct! The x-intercept is 600. This is the quantity the firm must produce and sell to break-even. The x-intercept is 5. This the price that the firm charges for each unit.

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An x x-intercept is where P(x)=0 P(x)=0. When profit is zero, we are at a break-even point for the firm. To find x x such that P(x)=0 P(x)=0, we set P(x)=0 P(x)=0 and solve: 5x−30005xx=0=3000=600. 5x−3000=05x=3000x=600. Question 15 0 / 1.66 pts Suppose that a town had a population of 12,500 in 2008 and the population has been growing at a constant rate of 4% per year since that time. Choose the expression that best represents the population in the year 2013. V=12500(1.05) 4 V=12500(1.05)4 V=12500(0.95) 4 V=12500(0.95)4 Correct Answer V=12500(1.04) 5 V=12500(1.04)5 You Answered V=12500(0.96) 5 V=12500(0.96)5 V=50000(1.05) 4 V=50000(1.05)4
The annual growth rate is 4% 4%. The correct exponential equation has the form Q=12500(1.04) t , Q=12500(1.04)t, where 12500 12500 is the initial population (in 2008) and t t is the number of years since 2008. For this example, t=5 t=5. Quiz Score: 20 out of 25

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Lesson 2 Quiz Attempt 1 Due Sep 13 at 11:59pm Points 25 Questions 15 Time Limit 75 Minutes Attempt History Attempt Time LATEST Attempt 1 55 minutes Score for this quiz: 18.34 out of 25 Submitted Sep 13 at 2:42pm This attempt took 55 minutes. Question 1 1.67 / 1.67 pts Solve for x: 12 e x4 =15 12ex4=15
ln( 152 ) ln(152) Correct! x=4ln30 x=4ln30 x= ln152 x=ln152 x= ln304 x=ln304 ln15ln2 ln15ln2 12e x4 e x4 x4x=15=30=ln30=4ln30 12ex4=15ex4=30x4=ln30x=4ln30 Question 2 1.67 / 1.67 pts A logistic function is a function of the form A1+Be −ct A1+Be−ct, where A,B,c A,B,c are constants. Given the logistic function Q(t)= 1001+Be −2t , Q(t)=1001+Be−2t, calculate the constant B B if f(0)=4 f(0)=4. B= 1003 B=1003

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B=25 B=25 Correct! B=24 B=24 B=99 B=99 B=49 B=49 f(0)=441+B1+BB=1001+Be −2⋅0 =1001+B=1004=25=24 f(0)=4=1001 +Be−2 04=1001+B1+B=10041+B=25B=24 Question 3 1.67 / 1.67 pts The population of trout in a lake decays exponentially over time due to fishing and can be modeled as P(t)=P 0 e −kt P(t)=P0e−kt, where t t is in years, P 0 P0 is the initial population, and k k is the decay constant. If the population is one-fourth the initial population after 5 5 years, calculate the decay constant k k. You may need to recall that −ln( 1x )=ln(x) −ln(1x)=ln(x). Correct! k= ln(4)5 k=ln(4)5 k=5ln(4) k=5ln(4)
k= ln( 14 )4 k=ln(14)4 k=ln( 54 ) k=ln(54) k=− ln(4)5 k=−ln(4)5 Solve for k k: 14ln(14)kk=e −5k =−5k=−15ln(14)=15ln(4) 14=e−5kln(14)=−5kk=−15ln(14 )k=15ln(4) Question 4 1.67 / 1.67 pts Suppose you invest \$8000 at an interest rate of 7%, compounded continuously. Calculate the time it will take, in years, for the value of the investment to grow to \$12,000. t= ln27ln3 t=ln27ln3 t=0.07ln(3/2) t=0.07ln(3/2) t= ln37ln2 t=ln37ln2 Correct! t= ln(3/2)0.07 t=ln(3/2)0.07

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t= ln120.07ln8 t=ln120.07ln8 For continuous compounding at rate r r, A=Pe rt A=Pert Here, P=\$8000 P=\$8000 and A=\$12,000 A=\$12,000. Solve for t t: Question 5 0 / 1.67 pts For the functions f(x)=lnx f(x)=lnx and g(x)=x 2 −3−−−−−√ g(x)=x2−3, calculate f(g(2)) f(g(2)).

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