Question

If f(x) is an exponential function where f(-1.5)=14 and f(4)=59, then find the value of f(1), to the nearest hundredth.

Answer 1

To find f(1), determine the constants for the exponential function using the given points, then evaluate f(1) with the found constants, rounding to the nearest hundredth.

Step-by-step explanation:

To find the value of f(1), we first need to determine the equation of the exponential function. Given two points (-1.5, 14) and (4, 59), we can set up two equations from the general exponential form f(x) = abx, where a is the initial value and b is the base of the exponent.

The two equations are:

1. 14 =
   `a *b^(-1.5)`
2. 59 =
   `a * b^(4)`

We can now solve this system of equations to find a and b. Dividing the second equation by the first gives us:

59/14 =
`(a * b^(4)) / (a * b^(-1.5))` =
`b^(5.5)`

Then b can be calculated, and subsequently a by plugging b's value back into either of the original equations. Once we have a and b, we can find f(1).

The value of f(1) will be a * b1, and we can round this to the nearest hundredth as the question asks.