IM Alg1.5.19 Lesson: Which One Changes Faster?
Here is a graph.
Which equation do you think the graph represents? Use the graph to support your reasoning.
What information might help you decide more easily whether the graph represents a linear or an exponential function?
A family has $1,000 to invest and is considering two options:
Bonds: How does the investment grow with simple interest?
Savings account: How are the amounts $999.60 and $1,019.59 calculated?
For each option, write an equation to represent the relationship between the amount of money and the number of years of investment.
Which investment option should the family choose? Use your equations or calculations to support your answer.
Use graphing technology to graph the two investment options and show how the money grows in each.
Complete the table of values for the functions f and g.
Based on the table of values, which function do you think grows faster? Explain your reasoning.
Which function do you think will reach a value of 2,000 first? Show your reasoning. If you get stuck, consider increasing by 100 a few times and record the function values in the table.
Consider the functions and . While it is true that , for example, it is hard to check this using mental math. Find a value of for which properties of exponents allow you to conclude that without a calculator.