Solve the problem.
-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 $$\mathrm { P } = \mathrm { k } \ln \left( \frac { 30 } { \mathrm { x } + 5 } \right) , 0 \leq \mathrm { x } \leq 25$$ where x is the percent of the region that has been paved. For a particular rural region, P = 1600
When x = 0. Predict what the quail population will be in this region when it becomes 5% paved.
Round your answer to the nearest whole number.
A) 0 quail
B) 1034 quail
C) 981 quail
D) 992 quail

Question

Quizplus · Accepted Answer

To find the quail population when x = 5, we first need to determine the constant k using the given condition P = 1600 when x = 0. Plugging these values into the formula, we get 1600 = k ln(30/5). Solving for k gives k = 1600 / ln(6). Now, substitute x = 5 into the formula: P = (1600 / ln(6)) ln(30/10). Calculating this gives approximately 981 quail.

Solve the Problem P=kln⁡(30x+5),0≤x≤25\mathrm { P } = \mathrm { k } \ln \left( \frac { 30 } { \mathrm { x } + 5 } \right) , 0 \leq \mathrm { x } \leq 25P=kln(x+530​),0≤x≤25

Solve the Problem $\mathrm { P } = \mathrm { k } \ln \left( \frac { 30 } { \mathrm { x } + 5 } \right) , 0 \leq \mathrm { x } \leq 25$