# Graphs and Functions Word Problems

Question 1 Multiple Choice

Question: The velocity of a particle is governed by the equation y = v(t) where t is in minutes and v(t) is in feet/minute. Find the distance this particle traveled during the first 5 minutes of its trajectory. (That is. find the distance traveled over [0, 5].)

v(t) = 2t2 + t

C' a) 93.33 feet

C b)83.S3feet

C c)55 feet

C d)95.833 feet

Question B Multiple Choice

Question: In preparing for your retirement in 40 years, you plan to contribute (at the end of each year) 10% of your annual salary to your company-provided 401(k) plan. You have chosen an investment option with a fixed rate of return of 8 % compounded continuously. Your starting salary is $35,000. You estimate that your annual salary will increase at the rate of approximately 5 percent per year. Thus your salary is given by the function y = S(t), where t is years.

(a) Determine how much money you will earn over 40 years.

(b) Assuming a continuous reinvestment of interest, what will your 401(k) retirement investment be worth at the end of 40 years? (Wnte out the integral, and then evaluate it either by hand or numerically using your calculator.) S(t) = 35000e^0.05t

C a) $1 .400,000 over 40 years. Your investment will be worth $ 3,434,544.23.

C b) You will earn $10,344,678.54 over 40 years. Your investment will be worth $3,434,544.23.

C c) You will earn $258,616.96 over 40 years. Your investment will be worth $85,863.86.

C d) You will earn $4,472,339.27 over4fl years. Your investment will be worth $4 853 .483.44.

Question 9

Multiple Choice

Question: Find the area between f(x) and g(x) from x = 0 to x = 2.

f(x)=2x and g(x)= x2

C a) 4 square units

C b) 413 square units

C c) 813 square units

C d) 2 square units

Question 10

Multiple Choice

Question: The following graphs represent the rate of change of sales (in hundreds of dollars per month) as a function of the month of two new salespeople, salesperson A and salesperson 6. (Assume these are the first 48 months on the job for each person.)

(i) Which salesperson sold more from zero to 24 months?

C a) Accumulated sales were equal from zero to 24 months and A sold more from zero to 48

months.

C b) A sold more from zero to 24 months and 6 sold more from zero to 48 months.

C c) S sold more from zero to 24 months and A sold more from zero to 48 months.

C d) S sold more from zero to 24 months and 6 sold more from zero to 48 months.

(ii) Which salesperson sold more from zero to 48 months?

#### Solution Summary

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