Let's say in five years, the scientist comes back to analyze the squirrel population because the science campus is expanding.
He finds that the squirrel population has stabilized around 945 squirrels. Using this data he calculates the r max to be 0.43. With the campus expanding, more area will be available for the squirrels to inhabit. What will the population size of squirrel be one year after the campus has expanded if it increases the carrying capacity to 1200? Assume r max does not change.

Given that the initial population size ($ N_0 $) is 945 squirrels, the maximum intrinsic growth rate ($ r $) is 0.43, and the time ($ t $) is 1 year after the campus expansion, we can calculate the population size ($ N_t $) using the new carrying capacity ($ K $) of 1200.

First, we need to calculate the growth rate ($ r $) using the formula for $ r_{max} $:

\[ r = r_{max} \times \left(1 - \frac{N_t}{K}\right) \]

Given $ r_{max} = 0.43 $, $ N_t = 945 $, and $ K = 1200 $, we can calculate $ r $:

\[ r = 0.43 \times \left(1 - \frac{945}{1200}\right) \]

\[ r = 0.43 \times \left(1 - 0.7875\right) \]

\[ r = 0.43 \times 0.2125 \]

\[ r = 0.091375 \]

Now, we can use this calculated growth rate ($ r $) in the exponential growth model formula to find the population size ($ N_t $) one year after the campus has expanded:

\[ N_t = 945 \times e^{0.091375 \times 1} \]

\[ N_t = 945 \times e^{0.091375} \]

\[ N_t ≈ 945 \times 1.0956 \]

\[ N_t ≈ 1035.192 \]

So, the population size of squirrels one year after the campus has expanded is approximately 1035 squirrels.

cameron029384 cameron029384 · Answer 2 · 2024-03-20T16:17:11+01:00

Answer:

The population size of squirrels one year after the campus has expanded with a carrying capacity of 1200 will be approximately 1350 squirrels.

Explanation:

To calculate the population size of squirrels one year after the campus has expanded with a carrying capacity of 1200, we can use the formula for exponential population growth:

Nt = N0 * (1 + r)^(t)

Where:

Nt = population size after time t

N0 = initial population size

r = maximum growth rate

t = time in years

Given that the initial population size is 945, the maximum growth rate (r) is 0.43, and the time is 1 year, we can calculate the population size after the campus has expanded:

Nt = 945 * (1 + 0.43)^(1)

Nt = 945 * (1.43)

Nt = 1350.15

Therefore, the population size of squirrels one year after the campus has expanded with a carrying capacity of 1200 will be approximately 1350 squirrels.