Suppose that a new employee starts working at $7.47 per hour and receives a 5 % raise each year. after time t, in years, his hourly wage is given by the equation y equals $ 7.47 left parenthesis 1.05 right parenthesis superscript t baseline. find the amount of time after which he will be earning $10.00 per hour.

Question

Bishop

Mathematics

25 October, 11:14

Suppose that a new employee starts working at $7.47 per hour and receives a 5 % raise each year. after time t, in years, his hourly wage is given by the equation y equals $ 7.47 left parenthesis 1.05 right parenthesis superscript t baseline. 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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Azul Abbott · Answer 1

For this case we have an equation of the form:

y = 7.47 * (1.05) ^ t

For y = 10 we have:

10 = 7.47 * (1.05) ^ t

From here, we clear the value of t.

We have then:

(1.05) ^ t = 10 / 7.47

log1.05 ((1.05) ^ t) = log1.05 (10 / 7.47)

t = log1.05 (10 / 7.47)

t = 5.978461004

Rounding off we have:

t = 6 years

Answer:

the amount of time after which he will be earning $ 10.00 per hour is:

t = 6 years