Answer:
y = 7*(2)^x
Step-by-step explanation:
We know that we have a function of the form:
y = a*b^x
Such that a and b are real numbers, and b also needs to be a positive number.
Such that this function passes through the points (3, 56) and (5, 224)
This means that:
56 = a*b^3
224 = a*b^5
So we have a system of two equations with two variables.
To solve this, we can take the quotient of the two equations (such that the second one is on the numerator) then we get:
(224/56) = (a*b^5)/(a*b^3)
4 = (a/a)*(b^5/b^3) = b^(5 - 3) = b^2
4 = b^2
Then we get:
√4 = b = 2
(because b needs to be positive we only care for the positive square root of 4)
The equation is something like:
y = a*(2)^x
Now we can use again the point (3, 56), so:
56 = a*(2)^3 = a*8
56 = a*8
56/8 = a = 7
Then the exponential equation is:
y = 7*(2)^x
