Question

In 1968, the U.S. minimum wage was $1.60 per hour. In 1978, the minimum wage was $2.65 per hour. Assume the minimum wage grows according to an exponential model w(t), where t represents the time in years after 1960. (a) Find a formula for w(t). (Round values to three decimal places.) w(t)

Answer 1

Answer:

Exponential equation is  

W(t) = $1.343* e^(0.022*t) ; where t = number of years from 1960

Step-by-step explanation:

Let’s assume W is minimum wage (in $) at time t, in years since 1960. Then W(o) is the  minimum wage in 1960; so exponential wage eqn. will be

W(t) = W(o)* e^(kt) ; where k is exponential constant

1.60 = W(o)* e^(k*8) -----1) ; in 1968 i.e. after t = 8 years, wages = $1.6

2.65 = W(o)* e^(k*18) ----2) ; in 1978 i.e. after t = 18 years, wages = $2.65

Divide eqn. 2 by 1, we get

2.65.....e^(k*18)

----- = ----------

1.6......e^(k*8)

1.656 = e^(10k)

Taking log on both sides

Log(1.656) = log (e^(10k))

0.219 = 10k

=>k = 0.022

now find W(o) by plugging this value in eqn. 1

1.60 = W(o)* e^(0.022*8)  

1.60 = W(o)*e^(0.175)

1.60 = W(o)*1.191

=> W(o) = $1.343 per hour

Exponential equation is  

W(t) = $1.343* e^(0.022*t) ; where t = number of years from 1960