Name

Math $1201$: Practice Exam $2$

August $12,2025$

$(20$ points$)$ A physics lab measures the light intensity $I(d)($in lux$)$ from a point light source at various distances $d($in meters$).$ The data is recorded in the table below.

$\backslash$table$[[d(m),0\mathrm{.}5,1\mathrm{.}0,1\mathrm{.}5,2\mathrm{.}0,2\mathrm{.}5,3\mathrm{.}0],[I(d)(lux),320,80,35\mathrm{.}6,20\mathrm{.}0,12\mathrm{.}8,8\mathrm{.}9]]$

$(6$ points$)$ Using the data, estimate the average rate of change of $I(d)$ from $d=1\mathrm{.}0$ m to $d=1\mathrm{.}5m.$ Include units.

$(7$ Points$)$ From part $1,$ interpret the meaning of the derivative $I^{\text{'}}(d).$

$(7$ Points$)$ Compare the average rate of change of $I(d)$ from $d=1\mathrm{.}5m$ to $d=2\mathrm{.}0$ m with the average rate of change from $d=2\mathrm{.}5m$ to $d=3\mathrm{.}0m.$ Does the data support that this function is linear? Why or why not?