1. The monthly income I, in dollars, from a new product is given by

I(t) = 7700 5500e^0.005t

where t is the time, in months, since the product was first put on the market.

(a) What was the monthly income after the 10^th month and after the 100^th month? (Round your answers to the nearest cent.)

I (10) =

I (100) =

b) What will the monthly income from the product approach as the time increases without bound? $ =

2. Lead shielding is used to contain radiation. The percentage of a certain radiation that can penetrate x millimeters of lead shielding is given by

I(x) = 100e^1.5x.

(a) What percentage of radiation, to the nearest tenth of a percent, will penetrate a lead shield that is 1 millimeter thick?

(b) How many millimeters of lead shielding are required so that less than 0.02% of the radiation penetrates the shielding? Round to the nearest millimeter.

3. A cup of coffee is heated to 180F and placed in a room that maintains a temperature of 80F. The temperature of the coffee after t minutes is given by

T(t) = 80 + 115e^0.042t.

(a) Find the temperature, to the nearest degree, of the coffee 10 minutes after it is placed in the room.

(b) Determine when, to the nearest tenth of a minute, the temperature of the coffee will reach 135F.