A conservation program is tracking the recovery of a native wildflower species in a national park. At the start of the program there are 200 plants. The number of plants is predicted to grow at a rate of 25% per year.
Let \(N\) = number of plants, and \(t\) = time in years.
- Complete the table of values below that models the growth of the plants. Round all answers to the nearest whole number. (2 marks)
\begin{array}{|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\quad t \quad \rule[-1ex]{0pt}{0pt}& \quad 0 \quad & \quad 1 \quad& \quad 2 \quad & \quad 3 \quad & \quad 4 \quad \\
\hline
\rule{0pt}{2.5ex}N \rule[-1ex]{0pt}{0pt}& 200 & & & & \\
\hline
\end{array}--- 3 WORK AREA LINES (style=lined) ---
- Using the table of values from (a), neatly plot the points and join with a smooth curve. (2 marks)
--- 0 WORK AREA LINES (style=lined) ---
a. \(\text{Table of values:}\)
\begin{array}{|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\quad t \quad \rule[-1ex]{0pt}{0pt}& \quad 0 \quad & \quad 1 \quad& \quad 2 \quad & \quad 3 \quad & \quad 4 \quad \\
\hline
\rule{0pt}{2.5ex}N \rule[-1ex]{0pt}{0pt}& 200 & & & & \\
\hline
\end{array}
b.
a. \(\text{Table of values:}\)
\begin{array}{|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\quad t \quad \rule[-1ex]{0pt}{0pt}& \quad 0 \quad & \quad 1 \quad& \quad 2 \quad & \quad 3 \quad & \quad 4 \quad \\
\hline
\rule{0pt}{2.5ex}N \rule[-1ex]{0pt}{0pt}& 200 & & & & \\
\hline
\end{array}
\(\text{Algebraic method}\)
\(\text{Formula: }\ N=200\times1.25^t\)
\(t=0:\ N=200\times1.25^{0}=200\)
\(t=1:\ N=200\times1.25^{1}=250\)
\(t=2:\ N=200\times1.25^{2}=312.5\approx313\)
\(t=3:\ N=200\times1.25^{3}=390.625\approx391\)
\(t=4:\ N=200\times1.25^{4}=488.28\ldots\approx488\)
\(\text{Using CASIO calculator with constant multiplier}\)
\begin{array} {|c|c|c|c|}
\hline t & \text{Input} & \text{Output}\ (N) & \text{Rounded}\ (N) \\
\hline \colorbox{lightblue}{0} & 200= & 200 & \colorbox{lightblue}{200} \\
\hline \colorbox{lightblue}{1} & \text{Ans}\times 1.25= & 250 & \colorbox{lightblue}{250} \\
\hline \colorbox{lightblue}{2} & = & 312.5 & \colorbox{lightblue}{313} \\
\hline \colorbox{lightblue}{3} & = & 390.625 & \colorbox{lightblue}{391} \\
\hline \colorbox{lightblue}{4} & = & 488.28\ldots & \colorbox{lightblue}{488} \\
\hline \end{array}
b.