We appreciate your visit to In an exponential function f x a b x it is known that f 5 15 and f 8 170 Which of the following is. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
To find the value of b, we can solve the system of equations formed by the given values of f(5) and f(8). By substituting the values of x in the exponential function, we can eliminate the constant factor and solve for b. The closest value to b is approximately 2.25, which corresponds to option b).
Explanation:
To find the value of b, we need to solve the system of equations formed by the given values of f(5) and f(8). We have:
- f(5) = 15: Substitute x = 5 in the exponential function to get a * b^5 = 15.
- f(8) = 170: Substitute x = 8 in the exponential function to get a * b^8 = 170.
Now, we can divide the second equation by the first equation to eliminate a:
Dividing a * b^8 = 170 by a * b^5 = 15, we get b^(8-5) = 170/15.
Simplifying the equation gives us b^3 = 34/3. To find b, we need to take the cube root of both sides: b = (34/3)^(1/3). Rounding this value gives us b ≈ 2.25, which is closest to the given options. Therefore, option b) is the closest value to the value of b.
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