(1) Functions of exponential growth For each of the following functions defined on [0, ∞), determine if it is of exponential type. Justify your answer. (a) et sin(t) (b)-et² (c) erf(t) (d) f(t)+g(t) where f(t) and g(t) are both of exponential type

The fox population in a certain region has an annualgrowth rate of 9 per year. In the year 2012, therewere 23,900 fox counted in the area. What is the foxpopulation predicted to be in the year 2020 ?

Continued This is a continuation of Exercise 13. As we saw earlier, the stock turnover rate of an item is the number of times that the average inventory of the item needs to be replaced as a result of sales in a given time period. Suppose that a hardware store sells 80 shovels each year. a. Suppose that the hardware store maintains an average inventory of 5 shovels. What is the annual stock turnover rate for the shovels? How is this related to the yearly number of orders to the wholesaler needed to restock inventory? b. What would he the annual stock turnover rate if the store maintained an average inventory of 20 shovels? c. Write a formula expressing the annual stock turnover rate as a function of the average inventory of shovels, identify the function and the variable, and state the units.

Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.

The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.

If xis large, which function grows faster, f(x)=2x or g(x)=x2?

Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.

Use a graphing utility to find an exponential regression formula f(x) and a logarithmic regression formula g(x) for the points (1.5,1.5) and (8.5,8.5). Round all numbers to 6 decimal places. Graph the points and both formulas along with the line y=x on the same axis. Make a conjecture about the relationship of the regression formulas.

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A culture of bacteria obeys the law of uninhibited growth.(a) If N is the number of bacteria in the culture and t is the time in hours, express N as a function of t.(b) If 500 bacteria are present initially and there are 800 after 1 hour, how many will be present in the culture after 5 hours?(c) How long is it until there are 20,000 bacteria?