Solve the problem. 1. A certain company has found that its expenditure rate per day (in hundreds of dollars) on a certain type of job is given by dE/dx = 2x + 5, where x is the number of days since the start of the job. Find the expenditure of the job takes 4 days. a. $36 b. $1300 c. $13 d. $3600 2. After a new firm starts in business, it finds that its rate of profits (in hundreds of dollars per year) after t years of operation is given by dP/dt = 3t^2 + 8t + 2. Find the profit in year 3 of the operation. a. $4850 b. $4500 c. $4100 d. $2800 3. Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time t, find the body's position at time t. a = 32, v(0) = -13, s(0) = -5 a. S = 16t^2 -13t b. S = 16t^2 -13t - 5 c. S = -16t^2 + 13t - 5 d. S = 32t^2 - 13t - 5 4. The charcoal from a tree killed in a volcanic eruption contained 68.4% of carbon of the carbon-14 found in living matter. How old is the tree, to the nearest year? Use 5700 years for the half-life of carbon-14. a. 1501 years b. 2165 years c. 5700 years d. 3123 years 5. A certain radioactive isotope decays at a rate of 2% per 400 years. If t represents time in years and y represents the amount of the isotope left, use the condition that y = 0.98y0 to find the value of K in the equation y = y0e^kt. a. 0.00005 b. -0.02020 c. 0.00666 d. -0.00005