M285_3.1_applications.pdf - Math 285 Modeling and Solving Differential Equation Applications N ha e k h l e e diffe e ial e a i le e where DEs are used

M285_3.1_applications.pdf - Math 285 Modeling and Solving...

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Math 285: Modeling and Solving Differential Equation Applications NRZ WhaW Ze kQRZ hRZ WR VRlYe VRPe diffeUeQWial eTXaWiRQV, leW¶V UeWXUQ WR a feZ aSSlied SURblePV where DEs are used and find solutions used to model each situation. Example 1: Models of Population Growth Remember that population growth is directly proportional to the original population, giving the DE: dP dt kP where k ! 0 and t is the time. a. Classify the DE. b. Solve for P ( t ) . (We¶Ye dRQe WhiV befRUe) c. Suppose it is known that the population of a town called Mathville increases at a rate proportional to the number of its inhabitants at time t. If the population of Mathville was 30,000 in 2000 and 48,000 in 2010, what will be the population in 2020? How fast was the population growing in 2015? Separable , ODE , linear , 1st order ptdp-kdtfpdp-fkdt-zlhlPI-kt-c.ee # ekt¥g * Find Ck k pets - - cekt 2010 10 48000 30000 - - cette ! # C ' 30000 1110148 480002 Pct ) : 30000 @ Kt ÷:÷ni :3 " .¥¥¥soo%e: = 76800 people in 2020 In in @ ' Ok ) dat .
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