Question

1. modeling real life the table shows the total u.s. biomass energy consumptions y (in trillions of british thermal units, or btus) t years after 2000. find a model for the data. use the model to estimate the total u.s. biomass energy consumption in 2017. example 3

Explanation:

Step1: Enter the data into a graphing calculator

Use the quadratic regression feature.

Step2: Obtain the quadratic model

The quadratic model is \(y = 6.8t^{2}+131.3t + 3005.8\)

Step3: Calculate \(t\) for 2017

Since \(t\) is years after 2000, for 2017, \(t=2017 - 2000=17\)

Step4: Substitute \(t = 17\) into the model

\(y=6.8\times(17)^{2}+131.3\times17 + 3005.8\)
First, calculate \(6.8\times(17)^{2}=6.8\times289 = 1965.2\)
Then, calculate \(131.3\times17=2232.1\)
Now, \(y=1965.2+2232.1 + 3005.8\)
\(y=1965.2+2232.1+3005.8=7203.1\)

Answer:

The model is \(y = 6.8t^{2}+131.3t + 3005.8\) and the estimated consumption in 2017 is \(7203.1\) trillion Btus.