Unit 5, Lesson 15

Using Graphs and Logarithms to Solve Problems (Part 1)

Algebra 2

Practice

Problem 1

The equation \(p(h) = 5,\!000 \boldcdot 2^h\) represents a bacteria population as a function of time in hours. Here is a graph of the function \(p\).

<p>Exponential growth function p of h = 5,000 times 2 to the power of h. Point on graph is about 4 point 4 comma 10,000. </p>

Use the graph to determine when the population will reach 100,000.
Explain why \(\log_{2} 20\) also tells us when the population will reach 100,000.

Problem 2

Technology required. Population growth in the U.S. between 1800 and 1850, in millions, can be represented by the function \(f\), defined by \(f(t) = 5 \boldcdot e^{(0.028t)}\), where \(t\) represents the number of years after 1800.

What does \(f\) estimate for the U.S. population in 1800?
Use graphing technology to graph the equations \(y=f(t)\) and \(y=20\). Adjust the graphing window to these boundaries: \(0< x< 100\) and \(0< y< 40\).
What is the point of intersection of the two graphs, and what does it mean in this situation?

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Using Graphs and Logarithms to Solve Problems (Part 1)

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7