A rich uncle wants to make you a millionaire. How much money must he deposit in a trust fund paying6% compounded quarterly at the time of your birth to yield $1,000,000 when you retire at age55? (Round your answer to the nearest cent.)$

A corporation recently sold zero-coupon $400 bonds maturing in 4 years with an annual yield of 12%. Find the price. [Hint: The price is the present value of $400 4 years from now at the stated interest rate.] (Round your answer to the nearest cent.)

A new car lists for $16,480 and depreciates by 45% per year. Find its value after the following amounts of time. (Round your answers to the nearest dollar.)

(a)2 years$

(b)3 months$

A covered mug of coffee originally at 220 degrees Fahrenheit, if left for t hours in a room whose temperature is 60 degrees, will cool to a temperature of

60 + 160e^1.9t

degrees. Find the temperature of the coffee after the following amounts of time. (Round your answers to the nearest degree.

(a) 45 minutes F (b) an hour F

An investment of $9000grows to $10,299.35in 4 years. Find the annual rate of return for annual compounding. [Hint: Use

P(1+r/m)^mt with m = 1 and solve for r (rounded to one decimal place)

R=%?

Hospitals use radioactive tracers in many medical tests. After the tracer is used, it must be stored as radioactive waste until its radioactivity has decreased enough for it to be disposed of as ordinary chemical waste. For the radioactive isotope iodine-131, the proportion of radioactivity remaining after t days is e^0.087t. How soon will the proportion of radioactivity decrease to 0.003 so that it can be disposed of as ordinary chemical waste? (Round your answer to the nearest day.)

The radioactive isotope potassium-40 is used to date very old remains. The proportion of potassium-40 that remains aftertmillion yearsis e^0.00054t. Use this function to estimate the age of the following fossil.A skeleton of an early human ancestor was discovered. Use the formula to estimate its age if rocks near the remains contained99.74% of their original potassium-40. (Round your answer to one decimal place.)

= million years

The proportion of students in a psychology experiment who could remember an eight-digit number correctly for t minutes was

0.9 0.4 ln(t) (for t > 1). Find the proportion that remembered the number for 9 minutes. (Round your answer to one decimal place.)

=%

The world's output of primary energy (petroleum, natural gas, coal, hydroelectricity, and nuclear electricity) is increasing at the rate of 2.4% annually. How long will it take to increase by 90%? (Round your answer to one decimal place.)

=yr

An investment grows at 24% compounded monthly. How many years will it take to do the following? (Round your answers to one decimal place.)

(a)double yr

(b)increase by 40% yr

Use the properties of natural logarithms to simplify the function.

f(x) = ln(11x) ln(11)

f(x) =

Use the properties of natural logarithms to simplify the function.

f(x) = ln(e^5x) 3x ln(1)

f(x) =