Exam 15: Algebraic Concepts 4

Use the fact that the quantity of a radioactive substance after t years is given by , where is the original amount of radioactive material and k is its half-life (the number of years it takes for half the radioactive substance to decay). The half-life of carbon-14 is 5600 years. Find the amount of carbon-14 remaining after 11,500 years if Round your answer to four decimal places if required.

If $P is invested for n years at rate i (as a decimal), compounded annually, the future value that accrues is given by , and the interest earned is Find I for the given P, n, and i. Round your answer to two decimal places. $1800 for 5 years at 10%.

Evaluate the following expression if it represents a real number.

Use the rules of exponents to simplify the expression.

Write the expression in radical form. Do not simplify.

Use the properties of exponents to determine the value for x that makes the equation true.

If an investment has a goal (future value) of $S after n years, invested at interest rate i (as a decimal), compounded annually, then the present value P that must be invested is given by Find P for the given S, n, and i. Round your answer to two decimal places. $24,000 after 10 years at 7.75%

Suppose it has been determined that the sales at Ewing Gallery decline after the end of an advertising campaign, with daily sales given by , where S is in dollars and x is the number of days after the campaign ends. What are the daily sales days after the end of the campaign?

Compute and simplify so that only positive exponents remain.

In calculus problems, the answers are frequently expected to be in a simple form with a radical instead of an exponent. Write the expression with radicals.

Evaluate the expression.

Use the properties of exponents to simplify the expression so that only positive exponents remain.

Use the properties of exponents to simplify the expression so that only positive exponents remain.

Compute and simplify so that only positive exponents remain.

Evaluate the following expression if it represents a real number.

Suppose the number of endangered species y can be approximated by the formula where t is the number of years past 1980. How many species does the formula estimate will be added to the endangered species list between 2007 and 2020? Round your answer to the nearest whole number.

Simplify the expression by using the properties of radicals. Assume nonnegative variables.

The intensity of sound I (as a multiple of the average minimum threshold of hearing intensity) is related to the decibel level D (or loudness of sound) according to . A decibel reading of 140 is at the threshold of pain. If is the intensity of this threshold and is the intensity when , express the ratio as a power of 10.

Use the properties of exponents to simplify the expression so that only positive exponents remain.

The intensity of sound I (as a multiple of the average minimum threshold of hearing intensity) is related to the decibel level D (or loudness of sound) according to . The background noise level of a relatively quiet room has a decibel reading of 34. Find the intensity of this noise level. Round your answer to three decimal places.