Question

Part A) A scientist begins with 100 milligrams of a radioactive substance that decays exponentially. After 31 hours, 50 mg of the substance remains. How many milligrams will remain after 58 hours? (Round your answer to two decimal places.)

Part B) Jamal wants to save $58,000 for a down payment on a home. How much will he need to invest in an account with 8.5% APR, compounding daily, in order to reach his goal in 5 years? (Round your answer to the nearest cent.)

Answer 1

Part A

The first order reaction rate is,

A(31) = 50 mg and A(0) =100 mg  Thus, we have,

For t=58 h, we have,

Thus, 27.33 mg of substance will remain.

Part B

Assuming 365 days in an year.

Total no. of days, n = 365 * 5 = 1825 days

Daily periodic rate, DPR = APR/365 = 8.5%/365= 0.02328767123%

Thus, Final amount, A= $58000

Let, initial amount be A_o

Then, we have,

A= A_o (1+ DPR)ⁿ

Putting in the values, we have,

Thus, the answer is $37,920.5