A worker is reviewing his pay increases over the past several years. The table below shows the hourly wage W, in dollars, that he earned as a function of time t, measured in years since the beginning of 2000. Time t Wage W 1 15.80 2 15.95 3 16.10 4 16.25 (a) By calculating ratios, show that the data in this table are exponential. (Round your answer to two decimal places.) ___________
A worker is reviewing his pay increases over the past several years. The table below shows the hourly wage W, in dollars, that he earned as a function of time t, measured in years since the beginning of 2000. Time t Wage W 1 15.80 2 15.95 3 16.10 4 16.25 (a) By calculating ratios, show that the data in this table are exponential. (Round your answer to two decimal places.) ___________
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 13DE
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A worker is reviewing his pay increases over the past several years. The table below shows the hourly wage W, in dollars, that he earned as a
| Time t | Wage W |
|---|---|
| 1 | 15.80 |
| 2 | 15.95 |
| 3 | 16.10 |
| 4 | 16.25 |
(a) By calculating ratios, show that the data in this table are exponential. (Round your answer to two decimal places.)
___________
(b) What is the yearly growth factor for the data? (Round your answer to two decimal places.)
___________
(c) The worker can't remember what hourly wage he earned at the beginning of 2000. Assuming that W is indeed an exponential function, determine what that hourly wage was. (Round your answer to the nearest cent.)
__________$
(d) Find a formula giving an exponential model for W as a function of t. (Round the parameters to two decimal places.)
(e) What percentage raise did the worker receive each year? (Use the model found in part (d).)
____________%
(f) Given that prices increased by 26% over the decade of the 2000s, use your model to determine whether the worker's wage increases kept pace with inflation.
___________
(c) The worker can't remember what hourly wage he earned at the beginning of 2000. Assuming that W is indeed an exponential function, determine what that hourly wage was. (Round your answer to the nearest cent.)
__________$
(d) Find a formula giving an exponential model for W as a function of t. (Round the parameters to two decimal places.)
W(t) = 15.64 × 1.01t
W(t) = 7.82 × 1.08t
W(t) = 19.55 × 1.91t
W(t) = 11.73 × 0.99t
W(t) = 31.29 × 1.04t
(e) What percentage raise did the worker receive each year? (Use the model found in part (d).)
____________%
(f) Given that prices increased by 26% over the decade of the 2000s, use your model to determine whether the worker's wage increases kept pace with inflation.
Yes, the wage increases kept pace with inflation rate.
No, the wage increases were lower than inflation rate.
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