An oil spill from a tanker in pristine Prince Williams Sound in Alaska begins in a circular shape only 2 ft across. what happens to the area if the diameter is doubling each hour. How large
will the spill be in 24 h?
diameter= 2^(t+1) t is time in hours.
Area= PI*radius^2= PI (diameter/2)^2
= 1/4 PI * 2^(t+1)
check my thinking.
I think i understand the diameter part which it would be:
D= 2(t+1)
2(24+1)
2x25
D=50
I do not understand the Area part though.
Notice the diameter is an exponent. ^means to the power of , as
2^(t+2) is the same as 2t+1
Area is related to diameter by the equation I gave.
Area= 1/4 PI * 2(t+1)
why don't you just do an example and let me check it?
ok so is the answer (2to the 24 power)squared times pi after 24 hours?
No. Area= 1/4 PI *(2t+1)^2
or Area= 1/4 PI (224+1)^2
or Area= 1/4 PI (250)
To understand what happens to the area of the oil spill as the diameter doubles each hour, we can use the formula: Area = 1/4 * PI * (diameter/2)^2.
In this case, the diameter is given by D = 2^(t+1), where t represents the time in hours.
Now, let's calculate the area of the oil spill after 24 hours:
D = 2^(t+1)
D = 2^(24+1)
D = 2^25
D = 50
So, after 24 hours, the diameter of the oil spill will be 50 feet.
Using the formula for area, we can find the area of the spill:
Area = 1/4 * PI * (2^(t+1))^2
Area = 1/4 * PI * (2^50)^2
Area = 1/4 * PI * 2^100
Area ≈ 1.57 * 10^31 square feet
Therefore, after 24 hours, the oil spill will cover an area of approximately 1.57 * 10^31 square feet.
Please note that this calculation assumes the oil spill maintains a circular shape as the diameter doubles each hour.