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 15.00 15.15 15.30 15.45 2 3 4 (a) By calculating ratios, show that the data in this table are exponential. (Round your answer to two decimal places.) The ratios of successive terms are always which shows that the data is exponential. (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.) $

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter7: Exponents And Exponential Functions
Section7.8: Transforming Exponential Expressions
Problem 1CYU
Question
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
1
2
3
4
Wage W
15.00
15.15
15.30
15.45
(a) By calculating ratios, show that the data in this table are exponential. (Round your answer to two decimal
places.)
The ratios of successive terms are always
(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.)
$
which shows that the data is exponential.
(d) Find a formula giving an exponential model for W as a function of t. (Round the parameters to two decimal
places.)
Ow(t)= 18.56 x 1.91
W(t) 14.85 x 1.01
0.99⁰
Ow(t) = 29.70 x 1.04
Ow(t) = 7.43 x 1.08
Ow(t) 11.14 x
W
(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.
Transcribed Image Text: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 1 2 3 4 Wage W 15.00 15.15 15.30 15.45 (a) By calculating ratios, show that the data in this table are exponential. (Round your answer to two decimal places.) The ratios of successive terms are always (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.) $ which shows that the data is exponential. (d) Find a formula giving an exponential model for W as a function of t. (Round the parameters to two decimal places.) Ow(t)= 18.56 x 1.91 W(t) 14.85 x 1.01 0.99⁰ Ow(t) = 29.70 x 1.04 Ow(t) = 7.43 x 1.08 Ow(t) 11.14 x W (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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