Area of Oil Spill = 2 square miles when time (t) = 0
Area of Oil Spill after 1 day = 2 x (1.21)
STEP 1: Establish the formula
Area of Oil Spill after t days = 2 x (1.21)^t (raised to the power of t)
STEP 2: If the area of the oil spill is 10 square miles, set the formula equal to 10.
10 = 2 x (1.21)^t
STEP 3: Take the logarithm of both sides
log 10 = log [2 x(1.21)^t]
1 = log (2) + t x log (1.21)
REASON: 10^1 = 10
the log of two amounts that are multiplied together equals the sum of the logs.
EXAMPLE: log (a x b) = log a + log b
And the log of an amount raised to a power is equal to that power times the log
EXAMPLE: log b^2 = 2 x log b
STEP 4: Find the log values of the numbers
log(2) = .3010 log (1.21) = .0828
STEP 5: Plug the log values into the formula
1 = .3010 + t x (.0828)
STEP 6: Subtract .3010 from each side of the equation
.699 = t x (.0828)
Step 7: Divide each side by .0828
t = 8.442
The answer is 8.442 days.
8/24/2014

Tracey M.
Comments
0 2.00
1 2.42
2 2.93
3 3.54
4 4.29
5 5.19
6 6.28
7 7.59
8 9.19
9 11.12
10 13.45