Exam 5: Exponential and Logarithmic Functions

How long will it take an investment of $4,000 to triple if the investment earns interest at the rate of 6% /year compounded daily?

Find the inflection points of the function .

Find the derivative of the function.

The change from religious to lay teachers at Roman Catholic schools has been partly attributed to the decline in the number of women and men entering religious orders. The percent of teachers who are lay teachers is given by where t is measured in decades, with corresponding to the beginning of 1960. Find the year when the percent of lay teachers was increasing most rapidly.

Find the derivative of the function.

An investor purchased a piece of waterfront property. Because of the development of a marina in the vicinity, the market value of the property is expected to increase according to the rule where V(t) is measured in dollars and t is the time in years from the present. If the inflation rate is expected to be 9% compounded continuously for the next 8 years, what is P(t) expected to be in 4 years?

Eleni, who is now 50 years old, is employed by a firm that guarantees her a pension of $20,000/year at age 60. What is the present value of her first year's pension if inflation over the next 10 year(s) is at the given rate. Assume that inflation is continuously compounded. Round your answers to the nearest cent. 5% $__________ 9% $__________ 11% $__________

Find the derivative of the function.

Evaluate the expression.

Find the derivative of the function.

Having received a large inheritance, a child's parents wish to establish a trust for the child's college education. If 5 year(s) from now they need an estimated $60,000, how much should they set aside in trust now, if they invest the money at the given rate of interest. 17.5% compounded quarterly _________ 17)5% compounded continuously _________

Strontium 90, a radioactive isotope of strontium, is present in the fallout resulting from nuclear explosions. It is especially hazardous to animal life, including humans, because, upon ingestion of contaminated food, it is absorbed into the bone structure. Its half-life is 27 years. If the amount of strontium 90 in a certain area is found to be four times the "safe" level, find how much time must elapse before an "acceptable level" is reached.

Based on data obtained from the Census Bureau, the manager of Plymouth Van Lines estimates that the percent of the total population relocating in year t ( corresponds to the year 1960) may be approximated by the formula . Compute , , and .

For children between the ages of 5 and 13 years old, the Ehrenberg equation gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 1.1 m to 1.4 m.

The percent of a certain brand of computer chips that will fail after t years of use is estimated to be . What percent of this brand of computer chips are expected to be usable after 3 years?

Find the inflection points of the function .

Use logarithms to solve the equation for t.

Eleni, who is now 55 years old, is employed by a firm that guarantees her a pension of $40,000/year at age 65. What is the present value of her first year's pension if inflation over the next 10 year(s) is at the given rate. Assume that inflation is continuously compounded. 4% _________ 8% _________ 19% _________

Use the laws of logarithms to simplify the expression.

Use the laws of logarithms to simplify the expression.