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| Growth Problems Online Math 124: Math for Liberal Arts Suzanne Miller, DVC Instructor |
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| Problem 1. |
note: the ^ symbol means 'raise to an exponent" A university keeps a number of mice for experiments. One day there were 89 mice, but three weeks later there were 127 mice. (this is the problem with exponential growth). a. develop a mathematical model that represent the population of mice as time passes. y=ae^bt the first pair of data time =0 --> (0,89) the first pair of data time = 3 weeks (3,127) STEP 1: find a (recall e^0 is 1) so 89 =ae^(b*0)=a and our equation becomes y = 89 e^bt to find b, put in secod pair of data --> 127 = 89 e^(3b) divide both sides by 89 --->127/89 = e^(3b) b= .118516 so model becomes --> y=89 e^(.118516 t) c. How many rats in 10 weeks? (t=10) y= 89(e^.118516x10) y=89x3.27121 = 291.13 rats. Is this a likely outcome? Should the school close for summer break leaving the rats with food? | |
| Problem 2. |
Home Value Appreciation
In July 1988 Alvarado bought a house for $189,000. In September 1989 a nearby, similar house sold for $207,000 Develop a mathematical model for the value of the house. STEP 1:what are the two data pairs? (0,$189,000) and (14 months,$207,000) STEP2: find the value of 'a' using t = 0 STEP 3: rewrite the equation using the value of a: STEP 4: find the value of 'b' using the second pair of data points. STEP 5. Rewrite the equation y= using the values of 'a' and 'b' STEP 6. Find the value of the house in Jan 1991. How many months since the purchase? Use that value for t=time. | |
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