Unit 7. Exponential and Logarithmic Functions Assignment

Exponential and Logarithmic Functions Assignment
Name________________________
Print this assignment and complete it showing all work.  
1. Complete the chart for the functions indicated. (4 marks)
Function domain range x-intercepts y-intercepts Sketch
 
y  2 log x

2. Solve the exponential equation 64x  83x  4 by changing the bases and then using algebra. (3 marks)
3. Trinh has decided to save money to buy a new computer. She invests $600 in an account that earns 5% per year, compounded quarterly. Determine how long she needs to invest her money to have $1000 by using the equation 1000  600(1.0125)n, where n is measured in quarters of a year (three-month increments).  (show work)  (2 marks)
4. A researcher has determined that an equation that models the height of a particular species of tree is y = 20.8 log(x), where y is height in metres and x is time in years. 
(2 marks)
a. Graph the equation using technology.
b. Predict how old the tree will be when it is 16 m tall.
5. Gallium-67 is used in nuclear medicine to help doctors locate inflammation and chronic infections. The patient is injected with a tracer (trace amount) that includes gallium-67, which collects in areas of inflammation and infection. The gallium-67 emits radiation that a special camera can detect. Gallium-67 has a half-life of 3.26 days. (3 marks)
a. Give an exponential equation to represent the percentage of the original gallium-67 after t days.
b. Solve your equation to determine the time it will take for there to be 2% of the original gallium-67.
6. Solve 124  3(4)2x – 1 for x using logarithms. (3 marks)
7. In a study, researchers found that the arterial blood pressure, P, in millimetres of mercury (mmHg) is related to the volume, V, of the blood vessel in microlitres (L). The data gathered is listed in the following table: (3 marks)
Arterial Blood Pressure, P (mmHg) Blood Vessel Volume, V (L)
70 0.63
100 0.80
120 0.86
140 0.90
160 0.94
a. Using a logarithmic regression, determine the equation that represents the relationship between blood pressure, P, and the blood-vessel volume, V.
b. Predict the blood-vessel volume when the arterial blood pressure is 130 mmHg. Make sure to round your answer to the nearest hundredth of a microlitre.
c. Predict the arterial blood pressure when the vessel volume is 0.7 L. Round your answer to the nearest millimetre of mercury.