Answered: Strontium 90 (Sr-90), a radioactive…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.1: Exponential Functions

Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...

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Question

Strontium 90 (Sr-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.

Find the function Q(t)that expresses the amount of Sr-90 present at time t, where Q₀is the amount present initially and t is measured in years.

Q(t) =

If the amount of Sr-90 in a certain area is found to be 16 times the "safe" level, find how much time (in years) must elapse before the safe level is reached.

Olivia plans to secure a 5-year balloon mortgage of $250,000 toward the purchase of a condominium. Her monthly payment for the 5 years is calculated on the basis of a 30-year conventional mortgage at the rate of 5%/year compounded monthly. At the end of the 5 years, Olivia is required to pay the balance owed (the "balloon" payment). What will be her monthly payment for the first 5 years, and what will be her balloon payment? (Round your answers to the nearest cent.)

monthly payment$

balloon payment$

Darla purchased a new car during a special sales promotion by the manufacturer. She secured a loan from the manufacturer in the amount of $23,000 at a rate of 4.2%/year compounded monthly. Her bank is now charging 6.5%/year compounded monthly for new car loans. Assuming that each loan would be amortized by 36 equal monthly installments, determine the amount of interest she would have paid at the end of 3 years for each loan. How much less will she have paid in interest payments over the life of the loan by borrowing from the manufacturer instead of her bank? (Round your answers to the nearest cent.)