MAT 1313 College Algebra- VC01 (6) Homework: SLO Homework (GELO)- Counts as two
ID: 3116191 • Letter: M
Question
MAT 1313 College Algebra- VC01 (6) Homework: SLO Homework (GELO)- Counts as two assignments Score: 167 of 10 pts HW Score: 24 24%, 267 of 11 pts Instructor-created question in 2002, a young couple bought their first house for $103,000 in 2014, they sold the house fo 100.000 Assuming the value of the house grows exponentially, wrt. model vio " vo ekt for the vaue of the house Let t +0 ropresent the year 2002 and assume the numbers sre r, thousands ef dotars (rut drop the last three zeros) The exponential modes vm» The value of the housen 2010 i. thousand dollarsExplanation / Answer
The exponential growth model for increase in the value of the house is V(t) = V0ekt, where V0 is the value of the house in 2002, V(t) is the price of the house t years after 2002 and k is a constant (growth rate).
(a). In 2002, the price of the house is $ 103000 which increases to $ 160000 in 2014 (i.e. when t = 12). Hence 160 = 103e12k ( on ignoring the last 3 zeros) or, e12k = 160/103. Now, on taking natural logarithm of both the sides, we get ln(e12k) = ln(160/103) or, 12k ln e = ln 160-ln 103 or, 12k = 5.075173815-4.634728988= 0.440444826 so that k = 0.440444826/12 = 0.036703735= 0.0367 ( on rounding off to 4 decimal places).
(b).The exponential growth model is V(t) = V0e0.0367t, where V0 is the price of the house in 2002, V(t) is the price of the house t years after 2002.
(c ). As per the above exponential growth model, the value of the house in 2018 is 103e0.0367*16 = 103e0.5873 = 103* 1.79912422 = 185.31 thousand dollars.
(d). If the growth model is linear, then the slope of the line is m = (160-103)/12 = 57/12.
(e). Since the value of the house, when x = 0, is 103, the y-intercept is 103. Hence the equation of the line in slope-intercept form is y = (57/12)x +103.
(f). In 2018, x = 16, so that the value of the house, as per the linear model is (57/12)*18+103 = (57*3/2)+103 = 188.5 thousand dollars.
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