The amount of water left in a cup after sitting outside in the sun can be modelled by the function A(t) = 120((12)^t/3 where A(t) represents the amount of water in mL and t represents the time passed in hours
a) write down how much water will be there after 24 hours. Round your answer to 2 decimal places.
b) write down how long it takes for the amount of water to get to 15 mL
See comment in your previous post of this
can u give link to that
I had stated :
"Check the typing of your equation.
The way it stands, it would be an increasing function, not representing the "amount of water left .." of your question."
I don't know why that reply did not show up.
Perhaps I didn't even click on "submit", need another coffee.
again? Why do you always start a whole new post when following up? And why do you not even correct your fractions and mismatched parentheses?
Clearly you should have written
A(t) = 120*(1/2)^(t/3)
(a) 24 hours is 8 half-lives, so 1/256 is left: 120/256 = ___
(b) now just solve
120*(1/2)^(t/3) = 15
15/120 = 1/8, so that is 3 half-lives, so t=9
To answer these questions, we need to substitute the given values into the function A(t) and solve for the unknown values.
a) To find the amount of water left after 24 hours, we can substitute t = 24 into the function A(t) = 120((12)^t/3 and solve for A(24):
A(24) = 120((12)^24/3
Calculating the exponent in the parentheses:
(12)^24 = 12^2 * 12^2 * ... * 12^2 (24 times) = 144 * 144 * ... * 144 (24 times)
Each multiplication of 144 is equivalent to squaring the previous number.
So, (12)^24 = 144^12
Substituting this back into the equation:
A(24) = 120(144^12/3
Now we simplify the right side:
A(24) = 120(12^12)
Calculating 12^12:
12^12 = 12^6 * 12^6 = 144^6
Substituting this back into the equation:
A(24) = 120(144^6)
Calculating 144^6:
144^6 = 331,776
Substituting this back into the equation, we get:
A(24) = 120(331,776)
A(24) = 39,813,120
Therefore, after 24 hours, there will be approximately 39,813,120 mL of water left in the cup. Rounded to two decimal places, this is equal to 39,813,120.00 mL.
b) To find out how long it takes for the amount of water to reach 15 mL, we need to substitute A(t) = 15 into the function A(t) = 120((12)^t/3 and solve for t:
15 = 120((12)^t/3
Divide both sides by 120:
15/120 = (12)^t/3
Simplify the right side:
0.125 = (12)^t/3
Multiply both sides by 3:
0.375 = (12)^t
Take the logarithm (base 12) of both sides:
log12(0.375) = log12((12)^t)
Using logarithm properties, we can simplify this equation:
log12(0.375) = t
Now, we calculate the logarithm using a calculator or math software:
log12(0.375) ≈ -0.845
Therefore, it takes approximately -0.845 hours (or about -50.7 minutes) for the amount of water to reach 15 mL. Note that the negative value indicates that it never reaches exactly 15 mL; it approaches but never reaches that value.