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Answer :
Final answer:
By dividing the given values of the exponential function at two different points, we can solve for the base 'b', which is found to be approximately 2.25.
Explanation:
To find the value of b in the exponential function f(x) = a(b)^x, we are given two points: f(5) = 15 and f(8) = 170. We can set up two equations based on this information:
- f(5) = a(b)^5 = 15
- f(8) = a(b)^8 = 170
By dividing the second equation by the first, we obtain:
(a(b)^8) / (a(b)^5) = 170 / 15
b^3 = 170 / 15
b^3 = 11.333...
To find the value of b, we take the cube root:
b = ∛(11.333...)
b ≈ 2.25
Therefore, the value closest to b is 2.25.
To find the value closest to b in the exponential function f(x) = a(b)^x, we can use the given information. We have two points on the graph of the function, (5, 15) and (8, 170). We can substitute these values into the function to get two equations.
The first equation is 15 = a(b)^5 and the second equation is 170 = a(b)^8. Now, we can solve these equations to find the value closest to b from the given options.
By substituting the first equation into the second equation, we get 170 = 15(b)^3. Dividing both sides by 15, we get 11.33 = (b)^3. Taking the cube root of both sides, we get b ≈ 2.25.
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