Quail are game birds that fare poorly when their habitat is encroached upon. Wildlife biologists have discovered that the population P of quail in a region is related to the percent of the region that has been paved with roads and parking lots,
According to the formula $$P = k \ln \left( \frac { 30 } { x + 4 } \right) , 0 \leq x \leq 26$$ where x is the percent of the region that has been paved. For a particular rural region, $P = 1600 \text { when } x = 0$ Predict
What the quail population will be in this region when it becomes 6% paved. Round your answer to the nearest
Whole number.
A) 883 quail
B) 925 quail
C) 0 quail
D) 872 quail

Question

Quizplus · Accepted Answer

First, find the value of $k$ using the given $P = 1600$ when $x = 0$: $1600 = k \ln \left( \frac{30}{0 + 4} \right)$. Solve for $k$ to use in the equation for $x = 6$. Then, calculate $P$ for $x = 6$ using the found value of $k$, rounding the result to the nearest whole number, which gives approximately 872 quail.

Quail Are Game Birds That Fare Poorly When Their Habitat P=kln⁡(30x+4),0≤x≤26P = k \ln \left( \frac { 30 } { x + 4 } \right) , 0 \leq x \leq 26P=kln(x+430​),0≤x≤26

Quail Are Game Birds That Fare Poorly When Their Habitat $P = k \ln \left( \frac { 30 } { x + 4 } \right) , 0 \leq x \leq 26$