Question

To find:The year in which the 2006 cost of tuition, room and board fees in public colleges will be doubled using the function f{{left({x}right)}}={13},{017}{left({1.05}right)}^{x}.

Math Word Problem
ANSWERED
asked 2021-02-03
To find:The year in which the 2006 cost of tuition, room and board fees in public colleges will be doubled using the function \(f{{\left({x}\right)}}={13},{017}{\left({1.05}\right)}^{x}\).

Answers (1)

2021-02-04
Concept:
Modeling is a method of simulating the real life situations with mathematical equations. Using these models we can forecast the future behavior. We can translate the mathematical word problem into a math expression using variables.
Calculation:
The given model is \(f{{\left({x}\right)}}={13},{017}{\left({1.05}\right)}^{x}\)
Where x is the number of years since 2006 and y = f(x) is the cost in dollars.
From the table, the average annual cost in 2006 is $12,837.
After xyears the 2006 will be doubled
So, After xyears, the cost will be \({2}\times{12837}=\${25674}\).
Hence, \(f{{\left({x}\right)}}={13},{017}{\left({1.05}\right)}^{x}={25674}\)
\({\left({1.05}\right)}^{x}=\frac{25674}{{13017}}\)
Taking natural logarithm on each side
\(\ln{\left({1.05}\right)}^{x}=\ln\frac{25674}{{13017}}\)
Using calculator, \({x}{\left({I}{n}{1.05}\right)}={0.679}\)
Divide by \(\ln{{1.05}},{x}=\frac{0.679}{ \ln{{1.05}}}\)
Using calculator, x = 13.92
Rounded off to nearest tens, \(x \approx 13\)
Hence, based on this model the 2006 cost will be doubled in 13 years since 2006.
That is, the year = 2006+13 = 2019
Final statement:
Hence, based on this model the 2006 cost will be doubled in 2019.
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-06-18
Who is more likely to binge drink—male or female college students? The Harvard School of Public Health surveys random samples of male and female undergraduates at four-year colleges and universities about whether they have engaged in binge drinking. What type of study design is being used to produce data?
asked 2021-01-25

The following table shows the average yearly tuition and required fees, in thousand of dollars, charged by a certain private university in the school year beginning in the given year.
\(\begin{array}{|c|c|}\hline \text{Year} & \text{Average tuition} \\ \hline 2005 & $17.6 \\ \hline 2007 & $18.1 \\ \hline 2009 & $19.5 \\ \hline 2011 & $20.7 \\ \hline 2013 & $21.8 \\ \hline \end{array}\)
What prediction does the formula modeling this data give for average yearly tuition and required fees for the university for the academic year beginning in 2019?

asked 2021-06-02
The table shows the populations P (in millions) of the United States from 1960 to 2000. Year 1960 1970 1980 1990 2000 Popupation, P 181 205 228 250 282
(a) Use the 1960 and 1970 data to find an exponential model P1 for the data. Let t=0 represent 1960. (c) Use a graphing utility to plot the data and graph models P1 and P2 in the same viewing window. Compare the actual data with the predictions. Which model better fits the data? (d) Estimate when the population will be 320 million.
asked 2021-01-04

Find the linear equations that can be used to convert an (x, y) equation to a (x, v) equation using the given angle of rotation \(\theta\).
\( \theta=\left\{\tan^{-1}\frac{5}{12}\right\}\)

...