Let's predict the number of dandelions in the population after 4 months. We start with an initial population of 40 individuals and a growth rate ([tex]\( r_{\text{max}} \)[/tex]) of 0.2 dandelions per month per capita. We'll calculate the population month by month, rounding to the nearest whole number at each step.
### Month 1
Initial Population: 40 dandelions
Individuals Added: [tex]\( 0.2 \times 40 = 8 \)[/tex]
Population After Month 1: [tex]\( 40 + 8 = 48 \)[/tex] dandelions
### Month 2
Population at the Beginning of Month 2: 48 dandelions
Individuals Added: [tex]\( 0.2 \times 48 = 9.6 \)[/tex]
Population After Month 2: [tex]\( 48 + 9.6 = 57.6 \rightarrow 58 \)[/tex] dandelions (rounded to the nearest whole number)
### Month 3
Population at the Beginning of Month 3: 58 dandelions
Individuals Added: [tex]\( 0.2 \times 58 = 11.6 \)[/tex]
Population After Month 3: [tex]\( 58 + 11.6 = 69.6 \rightarrow 69 \)[/tex] dandelions (rounded to the nearest whole number)
### Month 4
Population at the Beginning of Month 4: 69 dandelions
Individuals Added: [tex]\( 0.2 \times 69 = 13.8 \)[/tex]
Population After Month 4: [tex]\( 69 + 13.8 = 82.8 \rightarrow 83 \)[/tex] dandelions (rounded to the nearest whole number)
### Summary of Population Size Each Month
- Month 1: 48 dandelions
- Month 2: 58 dandelions
- Month 3: 69 dandelions
- Month 4: 83 dandelions
After 4 months, the population of dandelions is predicted to be 83 dandelions.
