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Mathematics - Algebra

Growth and decay problems:

1. GRIDDED ANSWER. A new laptop computer cost $2000. The value of the computer decreases overtime. The value V(in dollars) of the computer after t years is given by the function V=2000(0.82) raise to t. What is the decay rate, written as a decimal, of the value of the computer?

2. OPEN-ENDED. The value if a house in Iowa increased, on average, at a rate of bout 4% per quarter from the first quarter in 2001 to the last quarter in 2004. Write a function that models the value of the house overtime. Choose an initial value of the house and a quarter such that the value of the house is about $275,000.

3. EXTENDED RESPONSE. A musician is saving money to buy a new snare drum. The musician puts $100 in a savings account that pays 3% annual interest compounded yearly.
a. Write a function that models the amount of money in the account overtime.
b. Graph the function.
c. The musician wants a drum that costs $149.95. Will there be enough in the account after3 years? Explain.

4. MULTI-STEP PROBLEM. The half-life of a medication is the time it takes for the reduce to half of its original amount in a patient's bloodstream. A certain antibiotic has a half-life of about 8 hours.
a. A patient is administered 500 milligrams of the medication. Write a function that models the amount of the medication in that patient's bloodstream overtime.
b. How much of the 500 milligram dose will be in the patient's bloodstream after 24 hours?

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Growth and decay problems:

1. GRIDDED ANSWER. A new laptop computer cost $2000. The value of the computer decreases overtime. The value V(in dollars) of the computer after t years is given by the function V=2000(0.82) raise to t. What is the decay rate, written as a decimal, of the value of the computer?

V(t) = 2000(0.82)^t
V(0) = 2000(0.82)^0 = 2000 and V(1) = 2000(0.82)61 = 2000(0.82)
Change in the value = V(1) - V(0) = 2000(0.82) - 2000 = -360
Rate of change in value = -360/2000 = -0.18
This means the value "decays" by 0.18 (or 18%) every year.
The decay rate is 0.18.

2. OPEN-ENDED. The ...

Solution Summary

The growth and decay problems in mathematics is examined. Complete, Neat and Step-by-step Solutions are provided in the attached file.

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