IM Alg2.4.15 Lesson: Using Graphs and Logarithms to Solve Problems (Part 1)

Here is a graph that represents an exponential function with base , defined by . Explain how to use the graph to estimate logarithms such as .

Use the graph to estimate .

How can you use a calculator to check your estimate? What would you enter into the calculator?

The expression  models the balance, in thousands of dollars, of an account  years after the account was opened.  What is the account balance when the account is opened?

What is the account balance after 1 year?

What is the account balance after 2 years?

Diego says that the expression  represents the time, in years, when the account will have 5 thousand dollars. Do you agree? Explain your reasoning.

Suppose you opened this account at the beginning of this year. Assume that you deposit no additional money and withdraw nothing from the account. Will the account balance reach $1,000,000 and make you a millionaire by the time you reach retirement? Show your reasoning.

Noah is 15 years old and wants to retire a millionaire when he is 60. If he invests $1,000 today, what interest rate would he need to achieve this goal?

A population of cicadas is modeled by a function defined by  where  is the number of weeks since the population was first measured.  Explain why solving the equation  gives the number of weeks it takes for the cicada population to double.

How many weeks does it take the cicada population to double? Show your reasoning.

Use graphing technology to graph  and  on the same axes. Explain why we can use the intersection of the two graphs to estimate when the cicada population will reach 100,000.