Exam 10: Limits and the Derivative

Solve -The resale value R (in dollars) of a company car after t years is estimated to be given by What is the rate of depreciation (in dollars per year) after 4 years?

Provide an appropriate response. -Graph the function which calculates the present value of an amount of $5000 at an annual nominal rate of 7% compounded continuously for 0 c t c 10.Use the formula P = Ae-rt.

Provide an appropriate response. -Use graphical approximation methods to find the point(s) of intersection of f(x) = (ln x)² and to two decimal places.

Solve. -A single bacterium divides every 0.5 hour to produce two complete bacteria. If we start with a colony of 6000 bacteria, after t hours there will be A(t) = 6000 · 2^2t = 6000 · 4^t bacteria. Find A'(t) and A'(1).

Find f ' (x). -

Differentiate. - Find f'(t) for f(x) = (3x - 3) (3x³ - x² + 1)

Solve the problem. -How long will it take money to double if it is invested at 5.25%,compounded continuously? Round your answer to the nearest tenth.

Provide an appropriate response. -A man with $9000 to invest puts the money into an account that earns 8% compounded continuously.Graph the corresponding present value function and calculate the number of years before the $9000 will be due in order for its present value to be $7000.Use the formula P = Ae-rt.

Solve the problem. -Radioactive carbon-14 has a continuous compound rate of decay of r = -0.000124.Estimate the age of a skull uncovered at an archaeological site if 6% of the original amount of carbon-14 is still present.(Compute answer to the nearest year.)

Find the equation of the line tangent to the graph of f at the indicated value of x. -f(x) = 2 + ln x⁶; x = e

Solve the problem. -What will the value of an account (to the nearest cent)be after 8 years if $100 is invested at 6.0% interest compounded continuously?

Provide an appropriate response. -Find t to four decimal places.

Find f ' (x). -

Find the equation of the line tangent to the graph of f at the indicated value of x. -f(x) = 6 + ln x; x = 1

Solve the problem. -An investor buys 100 shares of a stock for $20,000.After 5 years the stock is sold for $32,000.If interest is compounded continuously,what annual nominal rate of interest did the original $20,000 investment earn? (Represent the answer as a percent to three decimal places.)

Solve the problem. -Suppose that $8000 is invested at an interest rate of 5.5% per year,compounded continuously.How long would it take to double the investment?

Provide an appropriate response. -Find t to four decimal places.e -0.07t = 0.05

Provide an appropriate response. -Use graphical approximation methods to find the point(s) of intersection of f(x) = ex and g(x) = x6 to two decimal places.

Find the equation of the line tangent to the graph of f at the indicated value of x. -

Solve -An experiment was set up to find a relationship between weight and systolic blood pressure in normal children. Using hospital records for 5000 normal children,the experimenters found that the systolic blood pressure was Given approximately by P(x)= 17.5(1 + ln x),10 ≤ x ≤ 100,where P(x)is measured in millimeters of mercury and x is measured in pounds.What is the rate of change of blood pressure with respect to weight at the 80-pound weight level?