Question

formula 3 points
the interaction between host and parasite (or predator and prey) can often lead to regular cycles. the duration of these cycles can be estimated using the following equation:
t=2π/√(rd)
let’s consider a host - parasite interaction where the host population shows a per - capita growth rate of 7.4 individuals per year, and the parasite population presents a death rate of 0.84. what is the oscillation time (in years) of this interaction? round your answer to two decimal places.
answer

Explanation:

Step1: Identify the formula and values

The formula for oscillation time \( T \) is \( T = \frac{2\pi}{\sqrt{rd}} \), where \( r = 7.4 \) (host per - capita growth rate) and \( d = 0.84 \) (parasite death rate).

Step2: Calculate the product \( rd \)

First, calculate \( rd=7.4\times0.84 = 6.216 \).

Step3: Calculate the square root of \( rd \)

Then, find \( \sqrt{rd}=\sqrt{6.216}\approx2.4932 \).

Step4: Calculate the oscillation time \( T \)

Now, use the formula \( T=\frac{2\pi}{\sqrt{rd}} \). Substitute the value of \( \sqrt{rd} \) into the formula: \( T = \frac{2\times\pi}{2.4932}\approx\frac{6.2832}{2.4932}\approx2.52 \) (rounded to two decimal places).

Answer:

\( 2.52 \)