Suppose that a new employee starts working at $7.65 per hour and receives a 5 % raise each year. After time t, in years, his hourly wage is given by the equation y=$7.65 (1.05) ^t. Find the amount of time after which he will be earning $10.00 per hour.

Question

Adalynn Singleton

Mathematics

16 March, 20:38

Suppose that a new employee starts working at $7.65 per hour and receives a 5 % raise each year. After time t, in years, his hourly wage is given by the equation y=$7.65 (1.05) ^t. Find the amount of time after which he will be earning $10.00 per hour.

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Answers (1)

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Coach · Answer 1

5.49 years

Step-by-step explanation:

y = $7.65 (1.05) ^t

You want to know for which value of t, y equals $10.

$10 = $7.65 (1.05) ^t

10/7.65 = 1.05^t

log (10/7.65) = log 1.05^t

log (10/7.65) = t (log 1.05)

t = [log (10/7.65) ] / (log 1.05)

t = 5.49