Question

12 mark for review the table presents values for a function ( f ) at selected values of ( x ). an exponential regression ( y = a b ^ { x } ) is used to model these data. what is the value of ( f ( 1.5 ) ) predicted by the exponential function model?

Explanation:

Step1: Input data into calculator

Use a calculator with an exponential regression function. Input the \(x\) - values \(-2,-1,1,2\) and the corresponding \(y = f(x)\) values \(10,15,40,56\).

Step2: Obtain regression equation

After running the exponential regression (\(y=ab^{x}\)), we get \(a\approx20.27\) and \(b\approx1.77\). So the equation is \(y = 20.27\times(1.77)^{x}\).

Step3: Calculate \(f(1.5)\)

Substitute \(x = 1.5\) into the equation \(y=20.27\times(1.77)^{1.5}\). First, calculate \(1.77^{1.5}=1.77^{\frac{3}{2}}=\sqrt{1.77^{3}}\approx\sqrt{5.54}=2.35\). Then \(y = 20.27\times2.35\approx47.6\).

Answer:

\(47.6\)