7. The population of a city can be modelled by the following equation: P=6t²+120t+3000 or P=6(t+10)²+2400 , where t represents the time in years and P represents the population. When t=0, the year is 2000.
a) What was the population in the year 2000?
b) What year is the population at its lowest point? What is the population during this time?
c) Which equation is more helpful to answer a)? Why?
d) Which equation is more helpful to answer b)? Why?
a) What was the population in the year 2000?
b) What year is the population at its lowest point? What is the population during this time?
c) Which equation is more helpful to answer a)? Why?
d) Which equation is more helpful to answer b)? Why?
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a) since 2000 is 0, plug in 0 so you are left with the population being 3000.
b) the vertex of the equation is at -10 because the second equation is in vertex form, so you look at the "k" value for y = a(x-h)^2 +k and k is 2400 so the year of the lowest point is 2000 - 10 which is 1990 and the population is 2400
c) the first equation because when u plug in 0, the constant is the only one with a value
d) the 2nd equation because you can easily see the vertex, the min/max point of the graph
b) the vertex of the equation is at -10 because the second equation is in vertex form, so you look at the "k" value for y = a(x-h)^2 +k and k is 2400 so the year of the lowest point is 2000 - 10 which is 1990 and the population is 2400
c) the first equation because when u plug in 0, the constant is the only one with a value
d) the 2nd equation because you can easily see the vertex, the min/max point of the graph
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a. set t = 0
P= 6t²+120t+3000
P = 3000 . ..answer
b. P=6(t+10)²+2400
Vertex at (-10, 2400) ---> (t, P)
hence, 2000 - 10 = 1990 . ..
P= 6t²+120t+3000
P = 3000 . ..answer
b. P=6(t+10)²+2400
Vertex at (-10, 2400) ---> (t, P)
hence, 2000 - 10 = 1990 . ..
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