Question

1) A radioactive substance decays exponentially. A scientist begins with 150 milligrams of a radioactive substance. After 26 hours, 75 mg of the substance remains. How many milligrams will remain after 46 hours?

2) A house was valued at $110,000 in the year 1988. The value appreciated to $155,000 by the year 2004.

A) What was the annual growth rate between 1988 and 2004?
r = ??? Round the growth rate to 4 decimal places.

B) What is the correct answer to part A written in percentage form?
r = %.

C) Assume that the house value continues to grow by the same percentage. What will the value equal in the year 2009 ?
value = $? Round to the nearest thousand dollars.

Answer 1

let amount = c e^(kt), where c is the starting amount, and t is in hours, and k is a constant.
In our case c = 150

given: when t = 26, amount = 75
75 = 150 e^(26k)
.5 = e^(26k)
26k lne = ln .5
26k (1) = ln .5
k = ln .5/26 = appr -.0266595

then:
amount = 150 e^(-.266595t)
so for t = 46
amount = 150 e^-1.2263373
= 44.005 mg

Use the same method for #2