On the first day of school, no students were sick. By the end of the first week, 12 students were sick, and by the end of the second week, 18 students were sick. The attendance clerk noticed that the number of students getting sick was growing exponentially with a growth factor of 1.5.

A function model that describes the number of students who have gotten sick is [tex]S(x) = 8(1.5)^x[/tex], where $x$ is the number of weeks completed at school.

Using this model, how many students could be expected to have been sick by the end of the 6th week?

Question

22-08-2023
Mathematics

High School

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On the first day of school, no students were sick. By the end of the first week, 12 students were sick, and by the end of the second week, 18 students were sick. The attendance clerk noticed that the number of students getting sick was growing exponentially with a growth factor of 1.5.

A function model that describes the number of students who have gotten sick is [tex]S(x) = 8(1.5)^x[/tex], where $x$ is the number of weeks completed at school.

Using this model, how many students could be expected to have been sick by the end of the 6th week?

Answer :

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TaylorSmith4590 TaylorSmith4590 · Answer 1 · 2024-02-05T16:02:36-05:00

61 students could be expected to have been sick by the end of the 6th week.

To use the exponential growth model to predict the number of students sick by the end of the 6th week, we'll plug in $ x = 6 $ into the function [tex]S(x) = 8 \times (1.5)^x \).[/tex]

[tex]\[ S(6) = 8 \times (1.5)^6 \][/tex]

[tex]\[ S(6) = 8 \times 1.5^6 \][/tex]

[tex]\[ S(6) = 8 \times 7.59375 \][/tex]

[tex]\[ S(6) = 60.75 \][/tex]

So, using the exponential growth model, we can expect approximately 60.75 students to be sick by the end of the 6th week.

Since you can't have a fraction of a student, you would round this to the nearest whole number.

Therefore, we can expect about 61 students to be sick by the end of the 6th week.

Complete question is given below:

At generic middle school 8 students were sick with the flu on the first day of school. By the end of the first week 12 students were sick and by the end of the 2nd week there were 18 students sick. The attendance clerk noticed that the number of students getting sick was growing exponentially with a growth factor of '1.5'. A function model that desribes the number that have gotten sick would S(x) = 8 (1.5*), where x is the number of weeks completed at school. Using the model, how many students could be expected to have been sick by the end of the 6th week?