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Interpret Graphs to Find Approximate Values

5.9.5 Interpret Graphs to Find Approximate Values

5.9.5 • Interpret Graphs to Find Approximate Values

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The graph shows the bacteria population on a petri dish as a function ff of the days dd since an antibiotic is introduced.

A line graph showing decreasing number of bacteria over 10 days, starting at 1,000,000 on day 0, with key points: (0, 1,000,000), (1, 900,000), and (2, 810,000). X-axis: time in days, Y-axis: number of bacteria.
1.

What is the approximate value of f(4.5)f(4.5)?

Compare your answer:

The exact value is 622,431, but reasonable approximations should be greater than 600,000 and less than 650,000.

2.

Approximately what is dd when f(d)=400,000f(d)=400,000?

Compare your answer:

The value to one decimal place is 8.7, but reasonable approximations should be greater than 8.5 and less than 9.

3.

Explain what you would do, using your usual graphing technology, to be able to see f(15)f(15) on the graph.

Compare your answer:

You may change xmax to 17, keeping all other window settings.

Discuss your explanation with a partner.

Why Should I Care?

A woman waters a plant with dollar coins growing from a jar filled with money and a small house, symbolizing investment or financial growth, with stacks of coins and dollar icons in the background.

Exponential functions and models can help you understand the power of investment.

Let’s say you invest $1000 in a stock that grows 10% every year. By the end of the first year, that money will grow and you will have $1100. The next year, the investment will grow again, based on the new amount. Your investment has compounded.

Now, imagine that money after 20 years: $7330!

Can you think of any other areas of your life where exponential functions and models can help you?