Question

1. what is the equation of the trendline? do not round, use exactly what excel calculates y = 1.5256e^{0.2018x}
2. how many billion of gallons will the us produce in the year 2022? show all work and round to the nearest tenth. y = 1.5256e^{0.2018(10)} y = 11.48

Explanation:

Step1: Identify the trend - line equation

The trend - line equation is given as $y = 1.5256e^{0.2018x}$.

Step2: Determine the value of $x$ for 2022

Assume that the base - year is 2012 (so when $x = 0$, it represents 2012), then for 2022, $x=2022 - 2012=10$.

Step3: Substitute $x$ into the equation

Substitute $x = 10$ into $y = 1.5256e^{0.2018x}$, we get $y=1.5256e^{0.2018\times10}$.
First, calculate the exponent: $0.2018\times10 = 2.018$.
Then, find the value of $e^{2.018}$. Since $e\approx2.71828$, $e^{2.018}\approx7.527$.
Multiply by the coefficient: $y = 1.5256\times7.527=11.48$.
Round to the nearest tenth: $y\approx11.5$.

Answer:

11.5