00:01
So in this question, we are given a function of two variables.
00:05
We're given a of r comma t.
00:09
This is equal to 1 ,000 times e to the power of rt.
00:16
And this is the amount of money that you would have at an interest rate of r % after t years.
00:25
And we're being asked to fill out a table here, right? and so let's make this table where we have our number of years.
00:36
So 5, 10, 15, 20.
00:41
This is my number of years.
00:44
So this is my t.
00:48
And then we have our rate could be 0 .08, 0 .12, 0 .10 first, actually, and then 0 .12.
01:00
Point 10, point 12, and point 14.
01:07
So this here is my rate.
01:11
It is r.
01:12
And so we are going to be evaluating 1000e to the rt at each of these 16 points.
01:21
And we're certainly going to use a calculator for this.
01:23
So let's start with an r of 0 .08 and use t values 5 through 20.
01:31
So, let's let's actually go to wolfram alpha, and i've already put in here f of rt, and we want this when r is 0 .08 and t is 5.
01:45
And i'll round to the new york dollar, $1 ,492, this says.
01:50
So in dollars, we're getting $1 ,492.
01:56
How about when r is 5 and t is 10? so if i let my t be 10, now i'm getting a final amount of $2 ,226.
02:10
$2 ,226.
02:13
How about if my t is 15, if my t is 15, my amount is $3 ,320.
02:25
$3 ,320.
02:27
And if my t is 20, if my t is 20, i'm getting an amount.
02:33
For $4 ,953.
02:37
$4 ,900, and $53.
02:40
And so now, let's move to an interest rate of 10%, and we'll start this exercise again.
02:47
Okay.
02:48
And so now let's make my r .1 .0 and my t5...