Answer:
[tex]\large \boxed{829}[/tex]
Step-by-step explanation:
We can use the exponential growth formula:
y = a(1 + r)ˣ
where
y = amount after x time
a = initial amount
r = growth rate as a decimal fraction
x = years since 2013
Data:
y = 2300
r = 0.12
x = 2022 - 2013 = 9
Calculations:
x = 2022 - 2013 = 9
[tex]\begin{array}{rcll}2300 &= &a(1.12)^{9} & & \\\ln 2300& = &\ln a+9 \ln1.12 & \text{Took the natural logarithm of each side}\\7.741 &= & \ln a + 9 \times 0.1133 & \text{Evaluated the logarithms}\\7.741 & = & \ln a + 1.020 & \text{Simplified}\\6.721 & = & \ln a & \text{Subtracted 1.020 from each side}\\\end{array}\\[/tex]
[tex]\begin{array}{rcll}e ^{6.721} & = & \ln a & \text{Took the anti ln of each side}\\a & = & \mathbf{829} & \text{Evaluated the function}\\\end{array}\\\text{The population affected by dengue in 2013 was $\large \boxed{\mathbf{829}}$}[/tex]
The figure below shows the growth curve for dengue victims since 2013
