## Linear function, Exponential function, word problem help

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

### Linear function, Exponential function, word problem help

I have a 3 part word problem, and I'm sure on most of the answers, but stuck at the end. Thank you in advance for any help.

Part 1: Mark comes home from vacation and finds out he has a serious rat problem. There is currently 317 rats in his house. After days of studying them, he determines they are increasing by 0.9% every day.
Assume that this is a linear function, find the equation and display in point-slope form.

I came up with the following:
Y1=317, Y2=319.853 (Let's assume there can be .853 rats for this equation), X1 = 0 (Current Day), X2 = 1 (Day 1)
Based on that: M=Y2-Y1 (2.583)/X2-X1 (1)
Solution: Y=2.853x+317
Correct?

Part 2: Mark has a very expensive record collection. He has numerous signed copies of Def Leppard, Shaquira, Ricky Martin, Jimi Hendrix and Beatles albums. The horde of rats have discovered this record collection. Mark has had the damage appraised and the rats have done approximately 17 million dollars worth of damaged and every day this number grows by 13%.
Assume that this is a linear function, find the equation and display in point-slope form.
Based on that: M=(19.21-17)/1-0 = 2.21
Solution: Y=2.21x+17
Correct?

Part 3:
Given the linear functions above, if we wanted to calculate the \$ damage per rat ratio and want it to increase at a constant rate of \$200 per day, what would this need to look like? Is it a quadratic or linear?
This is where I'm stuck.
I took the 17,000,000 and divided by the 317 rats to determine that on Day 0: Each rat is causing \$53627.76 worth of damage.
On the next day there are 319.853 rats (again, it's ok for there to be .853 rats in this case) and the damage done is 19,210,000: \$60058.84+200 = 60258.84

I'm pretty sure this one is not going to be a linear equation, but don't know how to express it. Any help is appreciated. Thanks for bearing(roar) with me.
somemathguy

Posts: 2
Joined: Thu Jan 09, 2014 2:11 pm

somemathguy wrote:Part 1: Mark...determines they are increasing by 0.9% every day.
Assume that this is a linear function

This makes no sense. "Increasing by 0.9% every day" is exponential growth, which cannot be "a linear function".

somemathguy wrote:every day this number grows by 13%.
Assume that this is a linear function

Same difficulty: exponential growth cannot be linear.

I can only suggest that you get VERY specific instructions regarding what, exactly, you're supposed to be doing here. Otherwise, there are loads of "right" answers, since any pair of points (the given point, plus any point on the exponential curve) could be used to create the linear model (so-called). Without knowing exactly how you're supposed to use a straight line to model something which is, by definition, not a straight line, I'm not even going to guess what "the" right (that is, the expected) answer might be.

stapel_eliz

Posts: 1797
Joined: Mon Dec 08, 2008 4:22 pm

### Re: Linear function, Exponential function, word problem help

I was thinking the same thing, but it specifically said linear function and that is why I went ahead and did it as so. I'll follow up with the professor again, thanks.
somemathguy

Posts: 2
Joined: Thu Jan 09, 2014 2:11 pm