Question

I need help interpreting this problem.

Jessie just finished the probation period at work and got a $0.50 per hour raise and 4 more hours of work per week. Jessie's friend scoffed, "That's only $2 more per week! Who cares?"

Why is Jessie's friend wrong about the change in Jessie's weekly pay? What more do we need to know about Jessie's work situation to calculate the actual change in the pay? How is this related to the product rule in calculus class?

Answer 1

Jesse needs to pick better friends. Even if it were only $2.00 / week, he shoudl be happy for his friend.

Jesse's friend is entirely overlooking the hours Jesse already worked.

I'll use 10 hours as the original working hours.
I'll use $5.00 / hour as the original wage.

10 hr * $5.00 / hr = $50.00

Move it up 4 hours and 50¢.

14 hr * $5.50 / hr = $77.00

$77-$50 = $27 - Substantially more than $2.00

Answer 2

haha! Makes sense now. So how does the product rule come into play with this problem? Or am I missing something so oblivious?

Answer 3

Well, let's see:

The change in the product of two things is the sum of these two things

1) The first multiplied by the change in the second
2) The second multiplied by the change int the first

In our case, we have

1) Original Hours multiplied by the change in the Wage Rate
2) Original Wage Rate multiplied by the change in the Original Hours

Let's see if it works, or if we're missing a piece.

1) 10 hrs multiplied by the $0.50 / hr = $5.00
2) $5.00 / hr multiplied by the 4 hrs = $20.00
3) Well, we are missing a little piece. Jesse's friend found the missing $2.00

It appears the comparison is not quite perfect.

Answer 4

it needs to be set up in equation form so if we set
x=original hours worked
y=original new per hour
xy=overall pay
new pay= (x+4)(y+0.5)
= xy+.5x+4y+2
increase= 0.5x+4y+2

there's the mising two dollars

Answer 5

how to relate this to the product rule is over my head

Answer 6

Can you please work the product rule out step by step?