Final answer:
To estimate the shadow's length after 95 minutes, a linear rate of change is calculated from the times and lengths given, resulting in an approximate shadow length of 39.6 cm.
Step-by-step explanation:
When analyzing how long the shadow of a stick will be after a certain amount of time, we can use the information provided to create a linear model. We know that after 20 minutes the shadow is 10.5 cm and after 60 minutes it is 26 cm long. Assuming a linear increase in shadow length over time, we can estimate the length of the shadow after 95 minutes.
First, we calculate the rate of change (slope) of the shadow length over time. The change in shadow length is 26 cm - 10.5 cm which equals 15.5 cm over a 40-minute period (from 20 to 60 minutes). Therefore, the slope is 15.5 cm / 40 min or 0.3875 cm/min.
Now that we have the rate of change, we can estimate the shadow length after 95 minutes from the original position (when the shadow length was 0 cm at time t=0). Since the shadow was 26 cm after 60 minutes, we will find the additional length after another 35 minutes (from 60 to 95 minutes) and add this to 26 cm. The additional length is 35 min × 0.3875 cm/min = 13.5625 cm. Adding this to the original 26 cm gives us an estimated shadow length of 39.5625 cm after 95 minutes.
Therefore, the estimated shadow length after 95 minutes is approximately 39.6 cm when rounded to one decimal place.