Answer :
To find out how many people had the flu at the beginning of the epidemic, we need to evaluate the function [tex]\( f(d) = 50 \cdot \left(\frac{3}{2}\right)^d \)[/tex] at the start, which means we look at when [tex]\( d = 0 \)[/tex].
Here's how we determine the number of people at the beginning:
1. Identify the Starting Point: The epidemic begins at day [tex]\( d = 0 \)[/tex].
2. Substitute [tex]\( d = 0 \)[/tex] into the Function: Replace [tex]\( d \)[/tex] in the equation with 0:
[tex]\[
f(0) = 50 \cdot \left(\frac{3}{2}\right)^0
\][/tex]
3. Calculate the Expression: Any number raised to the power of 0 is 1, so:
[tex]\[
\left(\frac{3}{2}\right)^0 = 1
\][/tex]
4. Multiply by the Initial Value: Multiply 50 by 1:
[tex]\[
f(0) = 50 \cdot 1 = 50
\][/tex]
Therefore, at the beginning of the epidemic, 50 people had the flu. Hence, the answer is 50.
Here's how we determine the number of people at the beginning:
1. Identify the Starting Point: The epidemic begins at day [tex]\( d = 0 \)[/tex].
2. Substitute [tex]\( d = 0 \)[/tex] into the Function: Replace [tex]\( d \)[/tex] in the equation with 0:
[tex]\[
f(0) = 50 \cdot \left(\frac{3}{2}\right)^0
\][/tex]
3. Calculate the Expression: Any number raised to the power of 0 is 1, so:
[tex]\[
\left(\frac{3}{2}\right)^0 = 1
\][/tex]
4. Multiply by the Initial Value: Multiply 50 by 1:
[tex]\[
f(0) = 50 \cdot 1 = 50
\][/tex]
Therefore, at the beginning of the epidemic, 50 people had the flu. Hence, the answer is 50.
