Which integer is 30 closest to
2 answers:
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You have to do this in quite a few steps. Your two points, written in coordinate form, are (4, 14) and (5, 16). The standard form for an exponential function is 
. Since neither one of these gives us an initial value of (0, a), we have to sub in the two points into 2 equations, creating a system that we can then solve for a, then b. Our system will look like this after we sub in the x and y values from each point. 
and 
. We need to solve for a and b. Let's solve for a first. Do that in each equation by dividing by the b^power: 
and 
. By the symmetric property, if equation 1 = a and equation 2 = a, then equation 1 = equation 2. So let's set them equal to each other: 
. Cross multiply to get 
. Now divide each side by the b with the lower exponent so we can cancel one of them out. 
. The b^4 cancels by the 16 and reduces by the 14 to leave you with this: 
, and b = 8/7, or 1.14 rounded. Now we will sub that in to one of our equations and solve for a. 
and 
Multiply both sides by 2401 to find that a = 8.21 rounded. So your exponential equation is 
. a = 8.21 is the growth factor.