Answer:
<u>The exponential model is: Cost after n years = 400 * (1 + 0.02)ⁿ</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Cost of the TV set in 1999 = US$ 400
Annual increase rate = 2% = 0.02
2. Write an exponential model to represent this data.
Cost after n years = Cost in 1999 * (1 + r)ⁿ
where r = 0.02 and n = the number of years since 1999
Replacing with the real values for 2020, we have:
Cost after 21 years = 400 * (1 + 0.02)²¹
Cost after 21 years = 400 * 1.5157
Cost after 21 years = $ 606.28
The TV set costs $ 606.28 in 2020.
<u>The exponential model is: Cost after n years = 400 * (1 + 0.02)ⁿ</u>
Interesting problem ...
The key is to realize that the wires have some distance to the ground, that does not change.
The pole does change. But the vertical height of the pole plus the distance from the pole to the wires is the distance ground to the wires all the time. In other words, for any angle one has:
D = L * sin(alpha) + d, where D is the distance wires-ground, L is the length of the pole, alpha is the angle, and 'd' is the distance from the top of the (inclined) pole to the wires:
L*sin(40) + 8 = L*sin(60) + 2, so one can get the length of the pole:
L = (8-2)/(sin(60) - sin(40)) = 6/0.2232 = 26.88 ft (be careful to have the calculator in degrees not rad)
So the pole is 26.88 ft long!
If the wires are higher than 26.88 ft, no problem. if they are below, the concerns are justified and it won't pass!
Your statement does not mention the distance between the wires and the ground. Do you have it?

Finding the radius,

Plugging in our values,

Rounding to the nearest whol number,


The answer is (3) -5 and 5.