Question

What is the answer?!?!?!

Answer 1

The equation D is the equation that best fits the data.

Why?

We can find the best option by substituting the easiest values into the given options.

Let's substitute f(0), f(1) and f(4) for each equation:

A.

$f(0)=3.02(3.67)^{0}=3.02$

$f(1)=3.02(3.67)^{1}=11.08$

$f(4)=3.02(3.67)^{4}=547.86$

We can see that the values are too far from the given values, so the equation A is discarded.

B.

$f(0)=2.27(2.09)^{0}=2.27$

$f(1)=2.27(2.09)^{1}=4.74$

$f(4)=2.27(2.09)^{1}=43.31$

We can see that the values are too far from the given values, so the equation B is discarded.

C.

$f(0)=8.04(0.98)^{0}=8.04$

$f(1)=8.04(0.98)^{1}=7.87$

$f(4)=8.04(0.98)^{4}=7.41$

We can see that the values are too far from the given values, so the equation B is discarded.

D.

$f(0)=6.61(1.55)^{0}=6.61$

$f(1)=6.61(1.55)^{0}=10.26$

$f(4)=6.61(1.55)^{0}=38.15$

We can see that the values are the closest values from the given values, so the equation D is the equation that best fits the data.

Have a nice day!