Question

y = 88.1x - 665\
y = 66(1.12)^x\
y = 9x^2 - 350x + 4000\
(a) which curve fits the data best?\
\bigcirc figure 1 \quad \boldsymbol{\bigcirc} figure 2 \quad \bigcirc 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.\
try one last time

Explanation:

Part (b)

Step1: Identify the best - fitting equation

From part (a), the best - fitting curve is Figure 2 with the equation \(y = 66(1.12)^{x}\). We need to find the value of \(y\) when \(x = 15\).

Step2: Substitute \(x = 15\) into the equation

Substitute \(x=15\) into the exponential function \(y = 66\times(1.12)^{15}\).

First, calculate \((1.12)^{15}\). Using a calculator, \((1.12)^{15}\approx5.473565759\).

Then, multiply this value by 66: \(y = 66\times5.473565759\).

\(y=66\times5.473565759 = 361.2553401\).

Step3: Round to the nearest hundredth

Rounding \(361.2553401\) to the nearest hundredth, we look at the thousandth place. The digit in the thousandth place is 5, so we round up the hundredth place.

\(361.2553401\approx361.26\)

Answer:

The predicted value of the item 15 years after its purchase is \(\boldsymbol{361.26}\).