Question

if ( ) f(x) is an exponential function where ( − 1.5 ) = 17 f(−1.5)=17 and ( 1.5 ) = 51 f(1.5)=51, then find the value of ( 2 ) f(2), to the nearest hundredth.

Answer 1

To find the value of f(2) for an exponential function with given values, set up equations using the given values and solve for the constants a and b. Then, substitute x = 2 into the equation to find f(2).

Step-by-step explanation:

To find the value of f(2), we can use the given information about the exponential function f(x).

Since f(x) is an exponential function, we can write it in the form f(x) = a * b^x, where a and b are constants.

Using the values given, we can set up two equations: 17 = a * b^(-1.5) and 51 = a * b^(1.5).

By solving these equations, we can find the values of a and b. Once we have the values of a and b, we can calculate f(2) by substituting x = 2 into the equation f(x) = a * b^x.

Answer 2

To find the value of f(2) for the given exponential function, we solve for the parameters 'a' and 'b' using the two points provided, then use these parameters to compute f(2) and round it to the nearest hundredth.

Step-by-step explanation:

The student is looking to determine the value of f(2) for an exponential function, given two points on the curve: f(-1.5)=17 and f(1.5)=51. To find this value, we can use the form of an exponential function, f(x) = ab^x, where 'a' is the initial value and 'b' is the base of the exponent. Since we have two points, we have two equations with two unknowns, which we can solve simultaneously to find 'a' and 'b'. Then, we can substitute these into the equation to find f(2).

Let's denote the two given points as (x1, y1)=(-1.5, 17) and (x2, y2)=(1.5, 51). Using the form of the exponential function, we have two equations:

1. 17 = a * b^(-1.5)
2. 51 = a * b^(1.5)

By dividing the second equation by the first, we can eliminate 'a' and solve for 'b'. After finding 'b', we can substitute it back into either equation to find 'a'. Once 'a' and 'b' are known, we can proceed to calculate f(2) = a * b^2.

However, as this is an approximation, it's important to remember that the rounding of numbers may affect the final value slightly. Once we have the calculated value, we will round to the nearest hundredth as per the student's instructions.