Answer do we just answer the question or we also have to do something else?
Step-by-step explanation:
Answer:
After about 9 minutes.
Step-by-step explanation:
We can write an exponential function to model the decay of Herodium-100.
We are given that it decreases by half every minute.
The standard exponential function is given by:
Where A is the initial amount, r is the rate, and m is the rate (in this case, in minutes).
Mathman initially has 2000 mL of Herodium-100. Therefore, A = 2000.
And since it decreases by half every minute, r = 1/2. Thus:
Mathman needs to rest when the Herodium-100 levels drop to 4 mL. Therefore, we can substitute 4 for f(m) and solve for m:
Solve for m. Divide both sides by 2000:
We can take the natural log of both sides:
By logarithm properties:
Therefore:
Mathman will have to rest and replenish after 9 minutes.
Find the first few
coefficients in the power series 4/1+4x^2.
Then we have:
4/ (1 – (-4x^2) = 4 Σ^ (n
≥ 0) (-4x ^2) ^n
= 4 (1 – 4x^2 + 4x^2 x^4 - … + (-4x ^2) ^n) These are the
first few coefficient of the series.
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Answer:
Step-by-step explanation: