WEBVTT
1
00:00:03.839 --> 00:00:06.669 A:middle L:90%
We're looking for an exponential function that goes with the
2
00:00:06.669 --> 00:00:08.359 A:middle L:90%
graph given, and we want it to be in
3
00:00:08.359 --> 00:00:10.369 A:middle L:90%
this form. But what we need to do is
4
00:00:10.369 --> 00:00:12.390 A:middle L:90%
find the value of C and the value of beat
5
00:00:13.039 --> 00:00:14.910 A:middle L:90%
. So let's use the ordered pairs we were given
6
00:00:14.910 --> 00:00:17.449 A:middle L:90%
and substitute them into the equation for X and Y
7
00:00:17.890 --> 00:00:21.940 A:middle L:90%
, and we get six equals C times be to
8
00:00:21.940 --> 00:00:25.750 A:middle L:90%
the first power when we substitute in the 0.16 and
9
00:00:25.750 --> 00:00:30.140 A:middle L:90%
we get 24 equal See times be to the third
10
00:00:30.140 --> 00:00:33.840 A:middle L:90%
power when we substitute in the 0.3 24 so we
11
00:00:33.840 --> 00:00:36.130 A:middle L:90%
can use this system of equations to solve for C
12
00:00:36.130 --> 00:00:38.890 A:middle L:90%
and B, Let's take the first equation. We
13
00:00:38.890 --> 00:00:41.100 A:middle L:90%
know that be to the first Power is just be
14
00:00:41.109 --> 00:00:44.829 A:middle L:90%
so we have six equals. C times be and
15
00:00:44.829 --> 00:00:47.009 A:middle L:90%
we can isolate. See in that equation and we
16
00:00:47.009 --> 00:00:50.950 A:middle L:90%
have C equals six divided by B. Now let's
17
00:00:50.950 --> 00:00:54.429 A:middle L:90%
use out for a substitution and let's substitute six divided
18
00:00:54.429 --> 00:00:56.649 A:middle L:90%
by B into the other equation where we have a
19
00:00:56.649 --> 00:01:00.549 A:middle L:90%
seat and that gives us 24 equals six divided by
20
00:01:00.549 --> 00:01:04.620 A:middle L:90%
B times be cubed. We can simplify that.
21
00:01:04.750 --> 00:01:07.950 A:middle L:90%
Be cubed over B is B squared. So we
22
00:01:07.950 --> 00:01:11.569 A:middle L:90%
have 24 equals six b squared. We can divide
23
00:01:11.569 --> 00:01:14.349 A:middle L:90%
both sides by six and we get four equals b
24
00:01:14.349 --> 00:01:15.849 A:middle L:90%
squared, and then we're going to square root Both
25
00:01:15.849 --> 00:01:19.469 A:middle L:90%
sites, typically, if we square root both sides
26
00:01:19.469 --> 00:01:21.810 A:middle L:90%
, we would write plus or minus two. But
27
00:01:21.810 --> 00:01:23.730 A:middle L:90%
the base in an exponential function has to be positive
28
00:01:23.969 --> 00:01:26.900 A:middle L:90%
. So we're only going to use the positive too
29
00:01:26.640 --> 00:01:29.040 A:middle L:90%
. Okay, so now we know one of the
30
00:01:29.040 --> 00:01:30.930 A:middle L:90%
two numbers we needed. We know the value of
31
00:01:30.939 --> 00:01:33.719 A:middle L:90%
B. Now let's move on and find the value
32
00:01:33.719 --> 00:01:36.469 A:middle L:90%
of C. Remember, we had see equal six
33
00:01:36.469 --> 00:01:40.530 A:middle L:90%
Overbey. So C equals six over to soc is
34
00:01:40.530 --> 00:01:42.140 A:middle L:90%
three. So putting all that together, we have
35
00:01:42.150 --> 00:01:47.079 A:middle L:90%
f of X equals three times two to the X
36
00:01:47.079 --> A:middle L:90%
power.