Question

running aroundproblem 1kiran was running around the track. the graph shows the time, t, he took to run various distances, d. the table shows his time in seconds after every three meters.| d | 0 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 || --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- || t | 0 | 1.0 | 2.0 | 3.2 | 3.8 | 4.6 | 6.0 | 6.9 | 8.09 | 9.0 |a. how long did it take kiran to run 6 meters?b. how far had he gone after 6 seconds?c. estimate when he had run 19.5 meters.d. estimate how far he ran in 4 seconds.e. is kirans time a function of the distance he has run? explain how you know.

Explanation:

Step1: Find t for d=6 (table)

From the table, when $d=6$, $t=2.0$

Step2: Find d for t=6 (graph/table)

From the graph/table, $t=6.0$ matches $d=18$

Step3: Estimate t for d=19.5

19.5 is halfway between 18 and 21. $t$ for 18=6.0, $t$ for 21=6.9. Estimate: $\frac{6.0+6.9}{2}=6.45$

Step4: Estimate d for t=4

From graph, $t=4$ matches $d\approx12$

Step5: Check function definition

Each distance $d$ has exactly one time $t$.

Answer:

a. 2.0 seconds
b. 18 meters
c. Approximately 6.45 seconds
d. Approximately 12 meters
e. Yes, it is a function. Each input (distance $d$) has exactly one output (time $t$), which satisfies the definition of a function.