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Suppose that when a certain lake is stocked with fish, the birth and death rates B and 8 are both inversely proportional to √P. 1 (a) Show that P(t)=kt +. JP.) ² (b) If Po=121 and after 4 months there are 289 fish in the lake, how many will there be after 8 months? (a) Find the differential equation dP dt = P a b P √P dP dt where k is a constant. where ß= a √P and 8= b √P

Suppose that when a certain lake is stocked with fish, the birth and death rates B and 8 are both inversely proportional to √P. 1 (a) Show that P(t)=kt +. JP.) ² (b) If Po=121 and after 4 months there are 289 fish in the lake, how many will there be after 8 months? (a) Find the differential equation dP dt = P a b P √P dP dt where k is a constant. where ß= a √P and 8= b √P

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that when a certain lake is stocked with fish, the birth and death rates ß and 8 are both inversely proportional to √P. Ŝ 2 + √PO) ². (b) If P=121 and after 4 months there are 289 fish in the lake, how many will there be after 8 months? (a) Show that P(t)=kt+√Po (a) Find the differential equation dP dt = P P(t) = sk my instructor a b √P JP F5 F6 h Now solve the differential equation with the initial condition P(0) = Po and find P(t). Do not substitute in the numerical value for Po- # 8 - F7 * O dP dt = + F8 8 where k is a constant. where B= F9 11 B a √P F10 + 11 www and 8 = √i Vi M b √P F11 ↓ F12 5. Clear all L PRTSC INS SCRLK Mare HOME Check answer PAUSE 8.3 PG UP NUM
Transcribed Image Text:Suppose that when a certain lake is stocked with fish, the birth and death rates ß and 8 are both inversely proportional to √P. Ŝ 2 + √PO) ². (b) If P=121 and after 4 months there are 289 fish in the lake, how many will there be after 8 months? (a) Show that P(t)=kt+√Po (a) Find the differential equation dP dt = P P(t) = sk my instructor a b √P JP F5 F6 h Now solve the differential equation with the initial condition P(0) = Po and find P(t). Do not substitute in the numerical value for Po- # 8 - F7 * O dP dt = + F8 8 where k is a constant. where B= F9 11 B a √P F10 + 11 www and 8 = √i Vi M b √P F11 ↓ F12 5. Clear all L PRTSC INS SCRLK Mare HOME Check answer PAUSE 8.3 PG UP NUM
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