Question

1. choose the correct answers. wildlife biologists were able to manage a hear of buffalo and increase the birth rate to 36% and decrease the death rate to 31%. there was an initial population of 75,000 buffalo. what is the difference between the birth rate and death rate? is this population in a state of growth or decay? write an exponential equation modeling the populations change over time. according to your model, what will the population of buffalo in this herd be in 10 years? a. decay b. $a(t) = 75,000(1.05)^t$ c. 122, 167 d. growth e. 5% f. 78, 750 g. 67% h. $a(t) = 75,000(0.95)^t$

Explanation:

Step1: Calculate rate difference

$36\% - 31\% = 5\%$

Step2: Determine growth/decay

Since birth rate > death rate, population grows.

Step3: Build exponential model

Growth factor = $1 + 0.05 = 1.05$, initial population $A_0=75000$.
$A(t) = 75000(1.05)^t$

Step4: Compute population at t=10

Substitute $t=10$ into the model:
$A(10) = 75000(1.05)^{10}$
$1.05^{10} \approx 1.6289$
$A(10) \approx 75000 \times 1.6289 = 122167.5 \approx 122,167$

Answer:

What is the difference between the birth rate and death rate? e. 5%
Is this population in a state of growth or decay? d. growth
Write an exponential equation modeling the population's change over time. b. $A(t) = 75,000(1.05)^t$
According to your model, what will the population of buffalo in this herd be in 10 years? c. 122, 167