Question

test information description instructions multiple attempts this test allows multiple attempts. force completion this test can be saved and resumed later. your answers are saved automatically. * question completion status: a moving to another question will save this response. question 6 during the early stages of an epidemic, the number of people that fall ill increases by 60% every 25 days. given this, what is the per - day rate of growth (the percent symbol, accurate to two decimal places (for example, if your answer is 12.6821%, you should input 12.68)).

Explanation:

Step1: Define the growth formula

Let the initial number of ill people be \( P_0 \), the number after \( t \) days be \( P(t) \), the daily growth rate be \( r \) (in decimal). The growth formula for compound growth is \( P(t)=P_0(1 + r)^t \). We know that in \( t = 25 \) days, the growth is \( 60\% \), so \( P(25)=P_0(1 + 0.6)=1.6P_0 \).

Step2: Substitute into the formula

Substitute \( t = 25 \) and \( P(25)=1.6P_0 \) into \( P(t)=P_0(1 + r)^t \):
\[
1.6P_0=P_0(1 + r)^{25}
\]
Divide both sides by \( P_0 \) (since \( P_0
eq0 \)):
\[
1.6=(1 + r)^{25}
\]

Step3: Solve for \( r \)

Take the 25th root of both sides. The 25th root of a number \( x \) is \( x^{\frac{1}{25}} \), so:
\[
1 + r = 1.6^{\frac{1}{25}}
\]
Calculate \( 1.6^{\frac{1}{25}} \). Using a calculator, \( 1.6^{\frac{1}{25}}\approx1.0183 \) (rounded to four decimal places). Then \( r\approx1.0183 - 1=0.0183 \). To convert to a percentage, multiply by 100: \( r\approx1.83\% \).

Answer:

1.83