A quantity starts at 29,000 and is exponentially decaying at the rate of 9% per month. What is left of that quantity after the 19th month has passed?
To solve this problem, we can use the exponential decay formula:
quantity = initial quantity x (decay rate)^(time)
In this case, the initial quantity is 29,000 and the decay rate is 9%, which we can express as 0.09. We want to find out what quantity is left after 19 months, so we plug in these values:
quantity = 29,000 x (0.91)^19
Using a calculator or computer program, we can evaluate this expression to find that the quantity left after 19 months is approximately 9,104. So only about 31.4% of the initial quantity remains.
Crystal has a headache, and takes 350mgbof Tylenol. The amount, A, of Tylenol remaining in her body after n hours is given by the formula A = 350 [0.71)n. How much if the Tylenol remains in her body after 6 hours? Round your answer to the nearest hundredth.
To find out how much Tylenol remains in Crystal's body after 6 hours, we plug in n=6 into the formula:
A = 350 [0.71)^6
A = 177.05
So approximately 177.05mg of Tylenol remains in her body after 6 hours. We round this to the nearest hundredth to get 177.05mg.
To calculate the amount remaining after the 19th month, we can use the formula for exponential decay:
A = P * (1 - r)^n
Where:
A = Final amount
P = Initial amount
r = Decay rate per time period
n = Number of time periods
Given:
P = 29,000 (Initial amount)
r = 9% per month (Decay rate)
n = 19 (Number of months)
Substituting these values into the equation:
A = 29,000 * (1 - 0.09)^19
Calculating the value inside the parentheses:
1 - 0.09 = 0.91
A = 29,000 * 0.91^19
Calculating 0.91 raised to the power of 19:
A ≈ 29,000 * 0.2292
A ≈ 6,651.25
Therefore, after the 19th month has passed, approximately 6,651.25 units of the quantity will be left.