The field mouse population satisfies the differential equationdpP450.dt2(b1). Find the time at which the population becomes extinct if p(0)the formula of general solution directly).=800 (you may use(b2). What is the minimal p(0) you can pick such that the mice won't extinct?(b3). If p(0) = 1000, what will happen? Does the solution p(t) look reasonable in reality?

Answered: The field mouse population satisfies…

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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5. When interest is compounded, the interest earned is added to the principal amount so that it may also earn interest. For a 1-year period, the principal amount Q is given by n i Q = (₁ + ²+ )" n Q (0) where i is the annual interest rate (given as a decimal) and n is the number of times during the year that the interest is compounded. Modeling with a Differential Equation tights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). sed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. To lure depositors, banks offer to compound interest at different intervals: semi- annually, quarterly, or daily. A certain bank advertises that it compounds interest con- tinuously. If $100 is deposited initially, formulate a mathematical…
(6) A bacterial culture contains y(0) grown to y(2) = 250[cells]. Construct and solve the differential equation assuming exponential growth. Determine the number of cells y(t) as a function of time. After how many hours does the bacterial culture 50[cells] at t O[hr]. After t = 2[hr], the bacterial culture has contain 2000 cells?
I would like this problem to be solved via Differential Equations. Thank you!Suppose you cool a pot of soup in a 75 °F room. Right when you take the soup off the stove, you measure its temperature to be 220 °F. Suppose after 20 minutes, the soup has cooled to 170 °F. Suppose you can eat the soup when it is 130 °F. How long will it take to cool to this temperature?
It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involed) and whether or not the equation is linear. Linearity is important because the structure of the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear for 2 3 and 4 it is also based on the drop down menu (in the picture)
As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the dx differential equation =1.6x-0.004x² (a) What is the maximum amount of the salt that will ever dissolve in the methanol? (b) If x=50 when t=0, how long will it take for an additional 50 g of salt to dissolve? (a) The maximum amount of the salt that will ever dissolve in the methanol is gijams. (Simplify your answer.) 5 AI 9 IN F5 F6 2 8 # B - U dt F7 → = ∞ A View an example Get more help. ↓ F8 H i 8 ↑ 2 e B F9 ↑ T' l Y F10 + + 1 8 *** F11 √i co Less F12 ● S Vi 2 Ө ÷ 1, A = Clear all L PRISC INS X U SCRLK - O HOME C V € Σ PAUSE PG UP 8 FR v -W. Check answer NUM (88) A S i x

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