Question

Let P represents the percentage of a city’s electrical power that is produced by solar panels t years after January 1, 2020.

(a) What does \(\frac{{{\bf{d}}P}}{{{\bf{d}}t}}\) represent in this context?

(b) Interpret the statement

\({\left. {\frac{{{\bf{d}}P}}{{{\bf{d}}t}}} \right|_{t = {\bf{2}}}} = {\bf{3}}.{\bf{5}}\)

Short answer

(a) The expression \(\frac{{{\rm{d}}P}}{{{\rm{d}}t}}\) represents the rate at which the electric power produced by solar panels changes with time.

(b) \({\left. {\frac{{{\rm{d}}P}}{{{\rm{d}}t}}} \right|_{t = 2}} = 3.5\) shows that after 2 years (after January 1 2020), solar panels percentage of electric power increased\(3.5\% \) per year.

Step-by-step solution

Interpret the meaning of \(\frac{{{\bf{d}}P}}{{{\bf{d}}t}}\)

The expression \(\frac{{{\rm{d}}P}}{{{\rm{d}}t}}\) represents the rate at which the electric power produced by solar panels changes with time. It was measured in percentage per year.

Interpret the meaning of \({\left. {\frac{{{\bf{d}}P}}{{{\bf{d}}t}}} \right|_{t = {\bf{2}}}} = {\bf{3}}.{\bf{5}}\)

The equation \({\left. {\frac{{{\rm{d}}P}}{{{\rm{d}}t}}} \right|_{t = 2}} = 3.5\) shows that after 2 years (after January 1 2020), the percentage of electric power produced by solar panels increased\(3.5\% \) per year.