A hiker is going to hike a mountain where there are four trails to the top of the mountain. In how many different ways can a per
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Answer:
or
Step-by-step explanation:
We are going to see if the exponential curve is of the form:
, (
).
If you are given the intercept, then
is easy to find.
It is just the coordinate of the
intercept is your value for
.
(Why? The intercept happens when
. Replacing
with 0 gives
. This says when
.)
So .
So our function so far looks like this:
Now to find we need another point. We have two more points. So we will find
using one of them and verify for our resulting equation works for the other.
Let's do this.
We are given is a point on our curve.
So when ,
.
Divide both sides by 8:
Reduce the fraction:
So the equation if it works out for the other point given is:
Let's try it. So the last point given that we need to satisfy is .
This says when ,
.
Let's replace with 2 and see what we get for
:
So we are good. We have found an equation satisfying all 3 points given.
The equation is .