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at the start of the covid-19 pandemic, some regions of the world were experiencing exponential growth in new daily cases. one model calculated that if the region had 4 new cases one day, it could expect to see ( c ) new cases ( t ) days later, according to the model:

( c(t) = 4(1.30)^t )

given this, what is the doubling time of new cases in this region? that is, in how many days can the region expect new cases of covid-19 to double? round accurate to the nearest day, and enter your answer as a number (no labels).

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question 1 of 10

Explanation:

Step1: Recall the doubling time formula for exponential growth

For an exponential growth model \( C(t)=C_0a^t \), the doubling time \( T \) is found by solving \( 2C_0 = C_0a^T \), which simplifies to \( 2 = a^T \). Taking the natural logarithm of both sides, we get \( \ln(2)=T\ln(a) \), so \( T = \frac{\ln(2)}{\ln(a)} \). In our model, \( C(t)=4(1.30)^t \), so \( a = 1.30 \).

Step2: Calculate the doubling time

Substitute \( a = 1.30 \) into the doubling time formula:
\( T=\frac{\ln(2)}{\ln(1.30)} \)
We know that \( \ln(2)\approx0.6931 \) and \( \ln(1.30)\approx0.2624 \).
So \( T=\frac{0.6931}{0.2624}\approx2.64 \)

Answer:

\( 2.64 \)