a)Calculating continuous growth

A person invests $100,000 at a nominal 12% interest per year compounded continuously. What will be the value of the

investment in 30 years?

b)Example 12

Calculating Continuous Decay

Radon-222 decays at a continuous rate of 17.3% per day. How much will 100 mg of Radon-222 decay to in 3 days?

Solution Since the substance is decaying, the rate, 17.3%, is negative. So, r = 0.173. The initial amount of radon-

222 was 100 mg, so a = 100. We use the continuous decay formula to find the value after t = 3 days:

A(t) = aert Use the continuous growth formula.

= 100e0.173(3) Substitute known values for a, r, and t.

59.5115 Use a calculator to approximate.

So 59.5115 mg of radon-222 will remain.

Try It #12

Using the data in Example 12, how much radon-222 will remain after one year?