Pregunta
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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.

Ask by Henry Martin. in the United States
Feb 26,2025

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To determine how many years it will take after 2020 to reach 2 million Franklin Trees, use the graphing calculator to find where the function \( f(t) \) equals 2. Plot \( f(t) \) and the line \( y = 2 \), then find their intersection point to get the required number of years.

Solución

To analyze the meaning of \( f \) in terms of the number of Franklin Trees per year (in millions), we first need to understand what \( f \) represents. Typically, in such contexts, \( f(t) \) could represent the population of Franklin Trees at time \( t \), where \( t \) is measured in years since a certain starting point (e.g., 2020). ### Step 1: Understanding \( f(t) \) Assuming \( f(t) \) is a function that models the growth of Franklin Trees, we can interpret \( f(t) \) as follows: - \( f(t) \) gives the number of Franklin Trees (in millions) at year \( t \). - For example, if \( f(0) = 1 \), it means there are 1 million Franklin Trees in the year 2020. ### Step 2: Finding the Year to Reach 2 Million Trees To determine how many years it will take after 2020 to reach a population of 2 million Franklin Trees, we need to solve the equation: \[ f(t) = 2 \] This means we need to find the value of \( t \) such that the function \( f(t) \) equals 2. ### Step 3: Using a Graphing Calculator To find the solution graphically, we can plot the function \( f(t) \) and look for the point where it intersects the line \( y = 2 \). 1. **Plot the function \( f(t) \)** on the graphing calculator. 2. **Draw the horizontal line** \( y = 2 \). 3. **Identify the intersection point** of the two graphs. ### Step 4: Calculation If you have the specific function \( f(t) \), please provide it so I can perform the calculations and find the exact year when the population reaches 2 million. If not, I can proceed with a general approach to find the intersection point. Please provide the function \( f(t) \) or any additional details needed to proceed.

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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!

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