Math Problem Statement

During the COVID- 19 pandemic, Arizona became one of the virus hotspots. On June 1 , 2020 , there were 1170 new positive cases reported. The next day (June 2 , 2020 ), there were 1309 new positive cases reported. (Note that these are new cases, not total cases reported during the pandemic.) Data were collected from the Arizona Department of Health Services.

The data are shown in the following table. DO NOT FILL IN THE TABLE UNTIL THE QUESTION ASKS YOU TO.

Number of days since June 1 , t Number of new positive cases reported 0 1170 1 1309 2 Incorrect 3 Incorrect 4 Incorrect Vanessa thought that maybe an exponential model would be more appropriate for predicting the number of new cases per day with respect to the number of days elapsed since June 1 .

There were Incorrect times as many positive cases on June 2 as on June 1 .

Incorrect Try again. Read the prompt carefully. Make sure you understand we are going to use an exponential model in this question. By what number do we need to multiply the number of new cases on one day to determine the number of new cases on the following day? This is an increase of ] Incorrect ] = undefined. (unmatched parens). percent in the number of new positive cases from June 1 to June 2 .

If the number of new cases per day increases by the same factor for the next several days, complete the table above predicting the number of new cases each day. [This will create an exponential function.]

Define a function g that predicts the number of new cases in Arizona reported t days after June 1 if we assume an exponential model. Be sure to use proper function notation.

Incorrect syntax error: this is not an equation

Incorrect Try again. Make sure you are entering the function notation correctly and using the correct variables. Also, make sure you recognize that we are assuming an exponential function to model this data. By what number do we need to multiply the number of new cases on one day to determine the number of new cases on the following day? Which of the following expressions represent the factor we multiply the number of new cases on one day by to get the number of new cases on the next day? Select all that apply.

f ( 4 ) f ( 0 )

f ( 2 ) f ( 1 )

f ( 1 ) f ( 0 )

f ( 2 ) − f ( 1 ) 2 − 1

f ( 4 ) − f ( 0 ) 2 − 0

f ( 3 ) − f ( 1 ) 3 − 1

Solution

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Math Problem Analysis

Mathematical Concepts

Exponential Growth
Multiplicative Factor

Formulas

Exponential function formula: g(t) = g(0) * r^t

Theorems

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Suitable Grade Level

Grades 10-12