1) Determine the time necessary for P dollars to double when it is invested at interest rate r compounded annually, monthly, daily, and continuously. (Round your answers to two decimal places.)

r = 1.7%

(a) annually yr (b) monthly yr (c) daily yr (d) continuously yr

2) The number of bacteria in a culture is increasing according to the law of exponential growth. After 2 hours, there are 200 bacteria, and after 4 hours, there are 800 bacteria. How many bacteria will there be after 6 hours? bacteria

3) Use the Richter scale

R = log

I

I₀

for measuring the magnitudes of earthquakes. Find the magnitude R of each earthquake of intensity I (let I₀ = 1). (Round your answers to two decimal places.)(a) I = 119,800,000 R = (b) I = 44,587,000 R = (c) I = 15,000 R =

4) Use the following information for determining sound intensity. The number of decibels of a sound with an intensity of I watts per square meter is given by

= 10 log(I/I₀),

where

I₀

is an intensity of

10¹² watt

per square meter, corresponding roughly to the faintest sound that can be heard by the human ear. Find the number of decibels of the sound.(a)

I = 10⁵ watt per m²

(busy street corner) dB (b)

I = 10⁸ watt per m²

(quiet radio) dB (c)

I = 10² watt per m²

(siren at 30 meters) dB (d)

I = 10² watt per m²

(jet at 30 meters) dB

5) Use the acidity model pH = log[H⁺], where acidity (pH) is a measure of the hydrogen ion concentration [H⁺] (measured in moles of hydrogen per liter) of a solution. Find the pH when [H⁺] = 1.62 10⁵. (Round your answer to two decimal places.) pH =

6) At 8:30 a.m., a coroner was called to the home of a person who had died during the night. In order to estimate the time of death, the coroner took the person's temperature twice. At 9:00 a.m. the temperature was 87.3F, and at 11:00 a.m. the temperature was 84.2F. From these two temperatures, the coroner was able to determine that the time elapsed since death and the body temperature were related by the formula

t = 10 ln

T 70

98.6 70

where t is the time in hours elapsed since the person died and T is the temperature (in degrees Fahrenheit) of the person's body. (This formula is derived from a general cooling principle called Newton's Law of Cooling. It uses the assumptions that the person had a normal body temperature of 98.6F at death, and that the room temperature was a constant 70F.) Use the formula to estimate the time of death of the person. (Round your answer to the nearest hour.) A.M.