Problem

The total number of people infected with a disease is growing at a rate of $5.4 \%$ per day. There are a total of 292 people infected today. Assuming the growth rate remains the same, write an equation that represents the total number of people, $T$, who will be infected with the disease $x$ days from now.
An equation that represents the total number of people who will be infected with the disease $x$ days from now is $T=$

Answer

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Answer

Final Answer: The equation that represents the total number of people who will be infected with the disease \(x\) days from now is \(\boxed{T = 292(1.054)^x}\).

Steps

Step 1 :This is a problem of exponential growth. The general formula for exponential growth is \(T = P(1 + r)^x\), where \(T\) is the total amount after \(x\) days, \(P\) is the initial amount, \(r\) is the growth rate, and \(x\) is the number of days.

Step 2 :In this case, \(P = 292\), \(r = 5.4\% = 0.054\), and \(x\) is the number of days from now.

Step 3 :We can substitute these values into the formula to get the equation that represents the total number of people who will be infected with the disease \(x\) days from now.

Step 4 :\(T = 292(1.054)^x\)

Step 5 :Final Answer: The equation that represents the total number of people who will be infected with the disease \(x\) days from now is \(\boxed{T = 292(1.054)^x}\).

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