Finite mathematics 1st year college homework help

Question

Hi I'm struggling with two questions and would love some help.

1. Brian requires 2100 calories per day to maintain his daily activities and to maintain a constant weight. He wants to gain weight. Each pound of body weight requires an additional 3300 calories. Write his daily calorie intake as a linear function of the number of pounds gained per day. (Let y represent the caloric intake and x represent the number of pounds gained.)

____________

2. The U.S. Department of Education estimated that the average annual cost (tuition, fees, room, and board) of attending a four-year private college or university was $21,855 in 2000 and $31,704 in 2008.

(a) Find the cost as a linear function of time since 2000. (Let y represent annual cost and x represent the year with 

x = 0 representing 2000. Round the slope to the nearest whole number.)

y = _______

 

(b) Use the linear function to estimate the cost in 2015. (Round your answer to the nearest whole number.)

$ _________

Answer 1

1.)

y= Calorie intake

x= number of pounds gained

2100 calories per day and 3300 calories per pound

Brian needs 2100 calories per day plus an additional 3300 calories per pound needed. To create a function to make this true, the 2100 calories per day would need to remain constant while the 3300 calories per pound can be adjusted. So the required linear function would be y= 3300x + 2100. With this all Brian would need to do is to decide how many pounds he would like to gain and then plug that number in for x and he can solve for how many calories he needs to take in per day. Brian can also decide how many calories he wants to take in per day and then plug that number in for y and he would be able to solve for how many pounds he would be gaining per day.

2.)

A.)

The linear function for A would be y= 1231x + 21,855. The way you solve for slope in this situation is to take the 31,704 (from 2008) and subtracting $21,855 (from 2000). 31,704 -21,855 = $9,849. Then take the $9,849 and divide by 8, representing the change in time from the one cost to the other and you will find the approximate price that it increased by per year. 9,849 / 8 = $1,231.125 ... and it says to round the slope to the nearest whole number so you would round it down to $1,231. Then in the function you add $21,855 because that is the base price given in the problem.

B.)

Estimate the cost in 2015. So this is real simple, the problem states to recognize 2000 as 0, and this is because it's the listed base year, so 2015 would be considered as 5. Then you would simply plug 5 in for x. y= 1231(5) + 21,855 ... This gives you an estimate cost in 2015 as $28,010.