6. Consider a bacteria culture growing exponentially, with time measured in hours. Suppose P (0) 100 cells is the initial size, and k = 0.03 is the relative growth rate. (a) Determine P (10), the population size at 10 hours. (b) Determine P' (10), the growth rate for the population at 10 hours. (c) At what time t will the population reach 20,000 cells? Include the units of measurement in your answers. =

You plan to invest in an account which pays 6.5% compounded continuously. If the investment period is for 8 years, then A(P) = Pe 0.065 •8 = Pe 0.52 gives the total balance of P dollars. a. Find a formula for A'(P). b. Find and interpret A'(8000). c. Compare the approximation to the actual change. a. A'(P) = e0.52 (Type an exact answer in terms of e.) b. A'(8000) = 1.68 dollars increased in the total amount per dollar increase in the initial investment (Round to the nearest cent as needed.) Interpret A'(8000) = 1.68 GA. The future value of a 9 year investment of $8000 will be $ more than the future value of a 9 year investment of S8000. O B. The future value of a 9 year investment of $8001 will be $ more than the future value of a 9 year investment of S8000. O C. The future value of 8 year investment of $8000 at 7.5% will be $ more than the future value of a 8 year investment of $4000 at 6.5%. D. The future value of a 8 year investment of $8001 will be $ 1.68 more than the future value…

The population of an aquatic species in a certain body of water is approximated by the logistic function 37,500 where t is measured in years. Find G(t) = = ,-0.56t' the population and its growth rate at the following times. a. 1 year b. 5 years c. 12 years d. What happens to the rate of growth over time? 1 + 12e The population in 1 year is 4774 . (Round to the nearest whole number.) The population in 5 years is 21680. (Round to the nearest whole number.) The population in 12 years is 36965. (Round to the nearest whole number.) The growth rate in 1 year is per year. (Round to the nearest whole number.)

A tree farm starts with ten trees. Tree growth is expected to follow logistic growth with a first-order growth rate constant of r = 0.16 yr ' to a maximum of 8,000 trees. Write the equation that relates the number of trees (N) to time (1). What are the values of No, r, and K? Plot the number of trees over time if no harvesting occurs. Go out to about 70 years. What is the maximum sustainable yield (MSY)? How long should you wait before harvesting at the MSY? Determine the standing crop. (The standing crop is the number of trees at steady state when harvesting at the MSY.)