Fe has been offered two jobs each with the same starting...

Fe has been offered two jobs, each with the same starting salary of 32,000 and identical benefits. Assuming satisfactory performance, she will receive a 1600 raise each year at the Company A, whereas the Company B will give her a 4% raise each year. a. In what year (after the first year) would her salary be the same at either company? Until then, which company pays better? After that, which company pays better? b. Answer the question in part (a) assuming that the annual raise at Company A is 2000.

Transcript

00:01 So in this problem, fee is getting job offers from companies, and she's got two companies, company a and company b.

00:12 And they both start, both have starting salary at $32 ,000.

00:24 Then company a does an annual pay raise of $1 ,600, whereas company b does 4%.

00:35 So then we're asked a series of questions.

00:41 First one is, in what year will they be the same again? obviously they're same at the start, but not after that.

00:55 Okay, well, company a over time pays us a $32 ,000 plus $1 ,600 per year, right? t is obviously in years here.

01:14 Company b pays us the 32 ,000 times 4 % per year.

01:31 So now the question becomes, when are these equal? okay, well, let's see.

01:39 If i take 32 ,000 plus 1 ,600 t, set that equal to 32 ,000 times 1 .04 to the t.

01:51 I can divide by 32 ,000, right, everywhere.

01:58 I get one plus i have 1 ,600 divided by a 32 ,000, is 0 .05t, is equal to 1 .04 to the t.

02:17 Okay.

02:19 And now let's take the natural log of both sides and see what happens.

02:27 So i have ln of 1 plus, oh no, see ln of 1 plus 0 .05 t is equal to t ln 1 .04.

02:48 Right? okay.

02:58 Let's see, how do we get to that t though? that's the question.

03:08 Well, this is going to be a little tough in it to get to.

03:13 But there's an easier way to do this.

03:16 So let's go to our graphing calculator and let's graph.

03:19 This for a minute okay and so i went to desmonds .com brought down the graphing calculator and i put in the first formula which was 32 ,000 plus 1600 x all right and let's change our parameters here let's do zero to say 20 on the x and the y then we'll start at 32 thousand and we'll go to 50 ,000...

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