05.06 Reasoning about Exponential Graphs (part 1)

Due No due date
Points 10
Questions 10
Time Limit None
Allowed Attempts Unlimited

Instructions

unit 5

Reasoning about Exponential Graphs (part 1)

Goal

You will examine the effect of changing a and b on a graph that represents $LaTeX: f\left(x\right)=a\cdot b^x$ . Then, apply that knowledge by answering questions.

Estimated completion time: 35 minutes

Watch

An exponential function can give us information about a graph that represents it.

For example, suppose the function q represents a bacteria population t hours after it is first measured and $LaTeX: q(t)=5,000\cdot(1.5)^t$ . The number 5,000 is the bacteria population measured when t is 0. The number 1.5 indicates that the bacteria population increases by a factor of 1.5 each hour.

A graph can help us see how the starting population (5,000) and growth factor (1.5) influence the population. Suppose functions p and r represent two other bacteria populations and are given by $LaTeX: p(t)=5,000\cdot2^t$ and $LaTeX: r(t)=5,000\cdot(1.2)^t$ . Here are the graphs of p, q, and r.

Graph with y-axis = number of bacteria and x-axis = time in hours. There are three lines gradually increasing in different ways but they all start at (0, 5000).

This graph cannot be easily described. If you need an explanation of this image, please ask your teacher for help.

All three graphs start at 5,000 but the graph of r grows more slowly than the graph of q while the graph of p grows more quickly. This makes sense because a population that doubles every hour is growing more quickly than one that increases by a factor of 1.5 each hour, and both grow more quickly than a population that increases by a factor of 1.2 each hour.

Watch the following video of reasoning about Exponential Graphs (part 1).

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