You are working part-time while going to college. The following table shows the hourly wage, w(), in dollars, that you earn as a function of time, t. Time is measured in years since the beginning of 2012 when you started working. Complete parts a through f. Time, t, Years, since 2012 Hourly Wage, w(t) (S) O1 2 3 4 5 11.50 12.19 12.92 13.70 14.52 15.39 a. Calculate the ratios of the outputs to determine whether the data in the table is exponential. Round each ratio to the nearest hundredth. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A The ratios are all approximately. so the data is exponential. (Type an integer or decimal rounded to the nearest hundredth O B. The ratios are not the same, so the data is not exponential. sneeded.) b. What is the growth factor? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA The growth factor is. (Type an integer or decimal rounded to the nearest hundredth as needed.) OB. The data has a decay factor. OC. Since the data is not exponential, there is no growth factor. c. Write an exponential model for the data in the table. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. wt) = (Use integers or decimals for any numbers in the expression. Round to the nearest hundredth as needed.) O B. Since the data is not exponential, there is no exponential model.
You are working part-time while going to college. The following table shows the hourly wage, w(), in dollars, that you earn as a function of time, t. Time is measured in years since the beginning of 2012 when you started working. Complete parts a through f. Time, t, Years, since 2012 Hourly Wage, w(t) (S) O1 2 3 4 5 11.50 12.19 12.92 13.70 14.52 15.39 a. Calculate the ratios of the outputs to determine whether the data in the table is exponential. Round each ratio to the nearest hundredth. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A The ratios are all approximately. so the data is exponential. (Type an integer or decimal rounded to the nearest hundredth O B. The ratios are not the same, so the data is not exponential. sneeded.) b. What is the growth factor? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA The growth factor is. (Type an integer or decimal rounded to the nearest hundredth as needed.) OB. The data has a decay factor. OC. Since the data is not exponential, there is no growth factor. c. Write an exponential model for the data in the table. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. wt) = (Use integers or decimals for any numbers in the expression. Round to the nearest hundredth as needed.) O B. Since the data is not exponential, there is no exponential model.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:You are working part-time while going to college. The following table shows the hourly wage, w(t), in dollars, that you earn as a function of time, t. Time is measured in years since the beginning of 2012 when you started working. Complete parts a through f.
Time, t, Years, since 2012
Hourly Wage, w(t) ($)
1
2
3
4
11.50 12.19 12.92 13.70 14.52 15.39
a. Calculate the ratios of the outputs to determine whether the data in the table is exponential. Round each ratio to the nearest hundredth. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The ratios are all approximately
so the data is exponential.
(Type an integer or decimal rounded to the nearest hundredth as needed.)
B. The ratios are not the same, so the data is not exponential.
b. What is the growth factor? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The growth factor is.
(Type an integer or decimal rounded to the nearest hundredth as needed.)
B. The data has a decay factor.
O C. Since the data is not exponential, there is no growth factor.
c. Write an exponential model for the data in the table. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
w(t) =
%3D
OA.
(Use integers or decimals for any numbers in the expression. Round to the nearest hundredth as needed.)
O B. Since the data is not exponential, there is no exponential model.
d. What percent raise did you receive each year?
The percent raise is % per year.
(Round to the nearest whole number as needed.)
e. If you continue to work for this company, what can you expect your hourly wage to be in 2027?
The expected hourly wage will be $.
(Type an integer or decimal rounded to the nearest hundredth as needed.)
f. For approximately how many years must you work for the company for your hourly wage to double? (Assume that you will receive the same percentage increase each year.)
years
(Round to the nearest whole number as needed.)
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