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Susan monitors the number of strep infections reported in a certain neighborhood in a given week.The recent numbers are shown in this table:WeekNumber of People020126234344According to her reports, the reported infections are growing at a rate of 30%.If the number of infections continues to grow exponentially, what will the number of infections bein week 10?

Susan monitors the number of strep infections reported in a certain neighborhood in a given weekThe recent numbers are shown in this tableWeekNumber of People02 class=

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SOLUTION

The formula for growth rate is given below;

[tex]y=a(1+r)^x[/tex]

Where;

y = number of infections,

a = initial number of infections (20),

r = rate (30% or 0.3) and

x = the week to find (10)

[tex]\begin{gathered} y=a(1+r)^x \\ y=20(1+0.3)^{10} \\ y\text{ = 20 (13.7858)} \\ y\text{ = 275.72} \end{gathered}[/tex]

The number of infections in week 10 will be 276.

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