rite an exponential function in the form y, equals, a, b, to the power xy=ab x that goes through the points left parenthesis, 0, comma, 8, right parenthesis(0,8) and left parenthesis, 2, comma, 288, right parenthesis(2,288).
Question
rite an exponential function in the form y, equals, a, b, to the power xy=ab x that goes through the points left parenthesis, 0, comma, 8, right parenthesis(0,8) and left parenthesis, 2, comma, 288, right parenthesis(2,288).
Solution
The general form of an exponential function is y = ab^x.
We know that the function passes through the points (0,8) and (2,288).
We can use these points to form two equations and solve for the values of a and b.
From the point (0,8), we substitute x = 0 and y = 8 into the equation, we get:
8 = ab^0 Since any number to the power of 0 is 1, we have a = 8.
Now we know the value of a, we can use the second point (2,288) to find the value of b. Substitute x = 2, y = 288, and a = 8 into the equation, we get:
288 = 8b^2 Divide both sides by 8, we get:
36 = b^2 Take the square root of both sides, we get:
b = 6
So, the exponential function that goes through the points (0,8) and (2,288) is y = 8*6^x.
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