8. We are making a growth chart for Amanda. At year t, her height in inches is h. a) typically we write points in this scenario as (t,h), not (h,t), why is that? b) on a horizontal axis, represent 3 things: t=6, t=10, and Δt=10-6 c) on a vertical axis, represent 3 things: h=45, h=54, and Δh=54-45 d) draw a reasonable sketch of h=f(t) which includes the points (6,45) and (10,54). Mark and label Δt and Δh for those two points on this graph. e) calculate that rate. If we assume the rate is constant, write the change equation for t and h f) suppose Amanda grew at that constant rate until age 12, what is her height? g) how long does it take for Amanda to grow 6 inches? Starting at age 11, at which age will she be 6” taller? h) if we swapped t and h (with t on the vertical axis so t=g(h)), what would the rate be (include units)?
8. We are making a growth chart for Amanda. At year t, her height in inches is h.
a) typically we write points in this scenario as (t,h), not (h,t), why is that?
b) on a horizontal axis, represent 3 things: t=6, t=10, and Δt=10-6
c) on a vertical axis, represent 3 things: h=45, h=54, and Δh=54-45
d) draw a reasonable sketch of h=f(t) which includes the points (6,45) and (10,54). Mark and label Δt and Δh for those two points on this graph.
e) calculate that rate. If we assume the rate is constant, write the change equation for t and h
f) suppose Amanda grew at that constant rate until age 12, what is her height?
g) how long does it take for Amanda to grow 6 inches? Starting at age 11, at which age will she be 6” taller?
h) if we swapped t and h (with t on the vertical axis so t=g(h)), what would the rate be (include units)?
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