Math Problem Statement

Enrollment in a school has grown exponentially since the school opened. A graph depicting this growth is shown. Determine the percentage rate of growth. (1 point)

Solution

To determine the percentage rate of growth from a graph depicting exponential growth, you typically need to extract two key points from the graph: the initial value (when the school opened) and the value after a certain period. However, since you haven't provided the graph, let's outline the general steps to calculate the percentage rate of growth:

  1. Identify Two Points on the Graph: You need to determine the population at two different times. Let these points be (t1,P1)(t_1, P_1) and (t2,P2)(t_2, P_2), where P1P_1 is the population at time t1t_1 and P2P_2 is the population at time t2t_2.

  2. Apply the Exponential Growth Formula: P(t)=P0ertP(t) = P_0 \cdot e^{rt} Here, P(t)P(t) is the population at time tt, P0P_0 is the initial population, rr is the growth rate, and tt is time.

  3. Calculate the Growth Rate rr: r=1t2t1ln(P2P1)r = \frac{1}{t_2 - t_1} \ln\left(\frac{P_2}{P_1}\right)

  4. Convert to Percentage: Multiply rr by 100 to get the percentage growth rate.

If you have the graph or specific values, I can calculate the growth rate for you.

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Math Problem Analysis

Mathematical Concepts

Exponential Growth

Formulas

Exponential Growth Formula: P(t) = P0 * e^(rt)

Theorems

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Suitable Grade Level

High School