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MATH SOLVE
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The total bear population in a certain area is represented by the function P=120(1.016)t , where t i...
5 months ago
Q:
The total bear population in a certain area is represented by the function P=120(1.016)t , where t is time in years. How would you rewrite this equation to identify the weekly growth rate of the population? How would you solve this equation.
Accepted Solution
A:
1) function: P = 120 (1.0160)^t, t in years
2) weekly function
w = 52 * t = 52t
=> P(w) = 120 (1.016)^ (52w)
3) growth rate = d P(w) / dw
d P(w) / dw = 120 * 52 * [ 1.016 ^ (52w) ] = 6240 [(1.016) ^ (52w) ]
4) solution of the equation
Separate variables
d P(w) = [ 6240 (1.016) ^ (52w)] dw
integrate from w = 0 until w
P(w) - Po = 7599.84 e ^ (0.82514w)
P(w) = Po + 7599.84 e ^ (0.82514w)