Answer: The rate = 8.5 ft/h
Step-by-step explanation:
Since we are going to need to differentiate to find the rate of change of θ we need to express it in radians rather than degrees.
Therefore, 15 degree per hour will be expressed as
15° × π/180 = 0.2618rad/hour
Using trigonometry function to find Ø
Tan Ø = 40/30 = 1.333
Ø = 53 degree
Convert it to radian
Ø = 0.93 rad
The changing at a rate of 15o per hour will be
Rate = radian/ time
0.2618 = (0.93 -0)/t
t = 0.93/0.2618
t = 3.5 hours
The rate of change in the length of the shadow at that same time will be:
Rate = 30/3.5 = 8.5 ft/ hour
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Answer:
a. Decay
b. 0.5
c. 4
Explanation:
If we have a function of the form
then
a = intital amount
b = growth / decay rate factor
x = time interval
If b > 1; then the equation is modelling growth. If b < 0, then the equation is modelling decay.
Now in our case, we have
Here we see that
inital amount = a = 4
b = 1/ 2 < 0, meaning the function is modeling decay
decay factor = b = 1/2
Therefore, the answers are
a. Decay
b. 0.5
c. 4
The answer is none of the above.
