Question

Help me find this answer please?

Answer 1

Option D

Explanation:

'Height h’ is plotted on the y-axis, which has units of ft. 'Years after planning’ is plotted on the x-axis, which has units of yr.

Rate of change is denoted by the slope or gradient m of the graph

m =
`(Rise)/(Run)`

Rise = Δy

= Change along the y-axis

= Difference in values along the y-axis

Run = Δx

= Change along the x-axis

= Difference in values along the x-axis

∴Rate of Change for this graph will have units of
`(ft)/(yr)`

The actual value can be calculated using coordinates of any two points along this graph

I used
`(2, 7)` as
`(x_(1) , y_(1))` and
`(3, 9.5)` as
`(x_(2) , y_(2))`:

m =
`(y_(2) - y_(1))/(x_(2) -x_(1))`

=
`((9.5 - 7) ft)/((3 -2) yr)`

=
`(2.5ft)/(1yr)`

∴ Rate of Change in tree’s height = 2.5
`(ft)/(yr)`

∴ Option D