What is the exponential function in the form #f(x)=ab^x# and has values: #f(1)=2# and #f(2)=5#?
2 Answers
Explanation:
Given:
The point
The point
We can temporarily eliminate the variable "a" and find the value of "b" by dividing equation [2] by equation [1]:
Substitute 5/2 for "b" in equation [1] and then solve for "a":
Substitute the values for "a" and "b" into
Here is the graph:
graph{(4/5)(5/2)^x [-10, 10, -6, 6]}
The answer is
Explanation:
Express the function you are trying to find as
Substitute
That is, where there is y, put in 2 and where there is x put in 1.
Now, we have
Then, substitute
That is, put 2 where we have x and 5 where we have y:
Now you need to solve these equations simultaneously. You could use the substitution method, but the most efficient method in this case is elimination. You can tell which method to use by assessing the equations you are given - use elimination if both equations are linear or if one term is eliminated one term when dividing the equation by the other. Substitution is generally used when you have several terms of various degrees.
Now then, divide equation 2 by equation 1:
using exponential laws,
This means that you have
Now take either of the points and plug it into the newly found equation. However, it is simpler, quicker and more efficient to take
Therefore,
Now we take the values of
You can check if this is true by taking one of the given x-values and plugging them in where there is x - you will get the corresponding y-value.