Jacob plans to work at his family's restaurant this summer to make some extra money. His parents have agreed to pay him $9.75 per hour to work Monday through Friday for a total of 10 weeks. They have also guaranteed that he can work at least 4 hours each day but no more that 7 hours per day. Describe the relationship between the amount of money jacob earns and the number of hours he works

There is a direct relationship between the amount of money that Jacob earns and the number of hours he works.

Step-by-step explanation:

In math, a direct relationship exists when a change in one variable causes another variable to change in the same manner. E.g. if variable X increases, then variable Y will increase. If variable X decreases, then variable Y will decrease.

In this case, if Jacob works 25 hours per week, he will earn $243.75. If he works 30 hours, he will earn $292.50. But if he only works 20 hours, he will earn $195.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: