Questions: The size of a rat population at the bay area of a certain city grows at a rate of 5% monthly. If there are 20 rats currently, find how many rats (rounded to the nearest whole) should be expected in 18 months. Use y=200(2.7)^(0.05 t), and let t be 18 months. y= rats.

The size of a rat population at the bay area of a certain city grows at a rate of 5% monthly. If there are 20 rats currently, find how many rats (rounded to the nearest whole) should be expected in 18 months. Use y=200(2.7)^(0.05 t), and let t be 18 months.
y= rats.

Transcript text: The size of a rat population at the bay area of a certain city grows at a rate of $5 \%$ monthly. If there are 20 rats currently, find how many rats (rounded to the nearest whole) should be expected in 18 months. Use $y=200(2.7)^{0.05 t}$, and let t be 18 months. $y=$ $\square$ rats.

Solution

Solution Steps

Step 1: Convert the growth rate into a decimal

The growth rate given is 5, which as a decimal is 0.05.

Step 2: Identify the parameters

Initial population size (P_0): 20 Base growth factor (r): 2.7 Growth rate (g) as a decimal: 0.05 Time period in months (t): 18

Step 3: Substitute the values into the formula

Using the formula $P(t) = P_0 \cdot r^{gt}$, we substitute the values to get $P(t) = 20 \cdot 2.7^{0.05 \cdot 18}$ After calculation, the future population size is 48.894.

Step 4: Round the result

Rounding the result to 0 decimal places, we get 49.