Question

choosing an exponential model and using it to make a prediction
(a) which curve fits the data best?
○ figure 1 ○ figure 2 ○ figure 3
(b) use the equation of the best fitting curve from part (a) to predict the value of the item at a time 15 years after its purchase. round your answer to the nearest hundredth.
$y = 66(1.12)^x$
$y = 9x^2 - 350x + 4000$
$y = 88.1x - 665$

Explanation:

Step1: Analyze the data - points' trend

By observing the data - points, the first figure with the exponential function $y = 66(1.12)^x$ seems to follow the upward - curving trend of the data best. The second figure is a quadratic function which has a different curvature pattern and the third is a linear function which does not capture the upward - curving nature of the data as well as the exponential function.

Step2: Use the best - fitting equation for prediction

The best - fitting equation is $y = 66(1.12)^x$. Substitute $x = 15$ into the equation. So, $y=66\times(1.12)^{15}$.
First, calculate $(1.12)^{15}$. Using a calculator, $(1.12)^{15}\approx5.473565755$.
Then, multiply by 66: $y = 66\times5.473565755\approx361.2553398\approx361.26$.

Answer:

(a) Figure 1
(b) $361.26$