Question

the minimum wage is established by the federal government. in 1938 the minimum wage was $0.25 per hour and it has risen to $7.25 per hour in 2009. Find an exponential function in the for, f(x)=ab^x

Answer 1

`0.25 = a b^0`

`a = 0.25`

So then our model is given by:

`y = 0.25 b^x`

Now using the second condition we know that x = 2009-1938 =71 so then we have this:

`7.25 = 0.25 b^(71)`

We can divide both sides by 0.25 and we got:

`(7.25)/(0.25)=29 = b^(71)`

And then solving for b we got:

`b = 29^(1/71)= 1.04856934`

So then our model would be given by:

`y = 0.25 (1.04856934)^x`

Explanation:

For this case we know that for 1938 the minimum wag was 0.25 per hour and for 2009 the new minimum wag was 7.25 per hour.

We want to find an exponential function like this:

`y = a b^x`

Where y represent the value for the minimum wage and x represent the number of years since 1938.

USing the first condition given we know that for 1938 the value of x = 0 and w ehave:

`0.25 = a b^0`

`a = 0.25`

So then our model is given by:

`y = 0.25 b^x`

Now using the second condition we know that x = 2009-1938 =71 so then we have this:

`7.25 = 0.25 b^(71)`

We can divide both sides by 0.25 and we got:

`(7.25)/(0.25)=29 = b^(71)`

And then solving for b we got:

`b = 29^(1/71)= 1.04856934`

So then our model would be given by:

`y = 0.25 (1.04856934)^x`