Population Growth The growth G of a population of lower organisms over a day is a function of the population size n at the beginning of the day. If both n and G are measured in thousands of organisms, the formula is
G= -0.03n exponent 2 plus n.

a. Make a graph of G versus n. Include values of n
up to 40 thousand organisms.

b. Calculate G(35) and explain in practical terms what your answer means.

c. For what two population levels will the population grow by 5 thousand over a day?

d. If there is no population to start with, of course there will be no growth. At what other population level will there be no growth?
Solve a only

Here is the graph of population growth \( G(n) \) versus the population size \( n \) (in thousands). The function \( G(n) = -0.03n^2 + n \) was plotted for values of \( n \) up to 40 thousand organisms. The graph shows how the population growth varies with the initial population size.

Would you like details about any part of the graph, or do you have any other questions?

Here are five related questions you might consider:
1. What happens to population growth as \( n \) increases beyond 40?
2. Why does growth decrease for larger populations?
3. How does the shape of the graph indicate maximum growth?
4. What is the significance of the intercepts on this graph?
5. How would changes in the coefficients of the equation affect the graph?

**Tip:** Pay attention to the regions where the graph crosses the axes — they often represent critical points, such as maximum growth or no growth.

Population Growth The growth G of a population of lower organisms over a day is a function of the population size n at the beginning of the day. If both n and G are measured in thousands of organisms, the formula is G = -0.03n^2 + n. a. Make a graph of G versus n. Include values of n up to 40 thousand organisms.

Learn how to graph the quadratic function G(n) = -0.03n^2 + n to model population growth in lower organisms. This example explains how growth changes with population size and highlights the key points of maximum growth and no growth. Suitable for students in Grades 9-12.

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