The number of students with cell phones in the city of Oakridge was 100 in the y
ID: 3029117 • Letter: T
Question
The number of students with cell phones in the city of Oakridge was 100 in the year 2000. The number of cell phones increased 224% annually.
a. What exponential function describes the number, y, of cell phones owned by high school students x years after 2000?
b. What is the equivalent logarithmic function? What do the independent and dependent variables for this function represent? Show how you developed the function.
c. Rewrite your answer to part (b) using the base 10 logarithm, log.
d. The Oakridge high school student population is relatively stable at 7200. Estimate the year in which all 7200 high school students in Oakridge will own a cell phone. Show how to determine the answer using the function.
Explanation / Answer
a) number of students = 100 in the year 2000
number of cell phones increased 224% annually
y = 100(2.24)^x
b) Take log on both side of
y = 100(2.24)^x
ln(y) = ln(100) + xln(2.24)
c) divide both sides by log10
log10(y) = log10(100) +xln10(2.24)
d) No. of cell phones = 7200
y = 100(2.24)^x
7200 = 100(2.24)^x
72 = 2.24^x
ln(72) = xln(2.24)
x = 5.3
It means year 2006