Download Pre-Calculus B Chapter 5 Content Quiz 9 Practice Calculator Name

Pre-Calculus B
Chapter 5 Content Quiz 9 Practice
Calculator
Name _____________________________
1. A nuclear scientist has a sample of 100 mg of a radioactive material which has a halflife in hours. She monitors the amount of radioactive material over a period of 30 hours
and obtains the following data.
Hours
0
5
10
15
20
25
30
mg
100
74.2
43.8
33.4
23.2
16.5
11.4
a. Use a graphing utility to fit an exponential function to the data. Round the values to
the nearest thousandth.
b. Use the function found in (a) to predict the amount of material, rounded to the nearest
tenth, remaining at 43 hours.
c. Use the function found in (a) to predict when the amount of radioactive material
reaches 12.3 mg. Round to the nearest hundredth.
2. After introducing an inhibitor into a culture of luminescent bacteria, a scientist
monitors the luminosity produced by the culture and obtains the following data.
Time, hours
2
3
4
5
8
10
15
Luminosity,
lumens
75.8
59.7
53.1
44.7
29
23.8
9.9
a. Use a graphing utility to fit a logarithmic function to the data. Round the values to the
nearest thousandth.
b. Use the function found in (a) to predict the luminosity, to the nearest hundredth, after
18 hours.
c. Use the function found in (a) to predict the number of hours needed for the luminosity
to become 13.5. Round to the nearest hundredth.
3. A mechanic is testing the cooling system in a boat engine. He measures the engine’s
temperature over time and obtains the following data.
Time,
minutes
5
10
15
20
25
Temperature,
°F
110
190
280
310
315
a. Use a graphing utility to build a logistic model from the data. Round the values to the
nearest thousandth.
b. Use the function found in (a) to predict the temperature after 12 minutes. Round to
the nearest hundredth.
c. Use the function found in (a) to predict the time, in minutes, that are required for the
temperature to reach 305°F. Round to the nearest tenth.