Analyze the meaning of \( f \) from part A. in terms of number of Franklin Tress per year (in millions). Then determine the number of years it will take after 2020 to reach a species of 2 million Franklin Tress. Use the graphing calculator to help explain.
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Bonus Knowledge
Let's break this down! When analyzing \( f \), it typically represents the growth function of Franklin Tress over time. If \( f(t) \) measures the population in millions of Franklin Tress at year \( t \), you can compare the function's outputs to understand its growth rate. If \( f(t) = 0.5t + 1 \), for example, by the year 2020 (where \( t=0 \)), there are \( 1 \) million Franklin Tress. To find when it will reach \( 2 \) million, set \( f(t) = 2 \) and solve for \( t \). You'd rearrange and solve the equation: \( 0.5t + 1 = 2 \). This simplifies to \( 0.5t = 1 \) or \( t = 2 \). Adding this to 2020, it means by the year 2022, we can expect to witness a lovely increase to 2 million Franklin Tress! To visualize this, using a graphing calculator to plot the function will show you how \( f(t) \) climbs. The x-axis represents the years (with 2020 as the starting point), and the y-axis covers the millions of Franklin Tress. The intersection of your \( f(t) \) curve and the line at \( 2 \) million showcases the exact point in time—super helpful for visual learners!