Answer: 0.87400mg of caffeine.
Step-by-step explanation:
You have
N(t)=N0(e^−rt)(1)
as a general Exponential decay equation where N0 is the amount at t=0, N(t) is the amount remaining at time t and r is the exponential decay constant. You're specifically given that after 10 hours, the decay factor is 0.2601, i.e.,
N(10)/N(0)=N0(e^−10r)/N0(e^0)= e^−10r=0.2601 . .(2)
Taking the last 2 parts of (2) to the power of 0.1t gives
e^−rt=0.2601^.1t . .(3)
This means that
N(t)=N0(e^−rt)=N0(0.2601^.1t). .(4)
Also,
N(2.56)N(1.56)=N0(0.2601.1(2.56))N0(0.2601.1(1.56))=0.2601.1(2.56−1.56)=0.2601^.1
= 0.87400mg of caffeine.
Answer:
f(x) = 2x + 4
Step-by-step explanation:
This is an arithmetic sequence
y = a1 + (x - 1)d where a1 = first term and d = common difference so it is
y = 6 + (x - 1)*2
y = 2x + 4 answer
Answer: 6 and 1/4
Step-by-step explanation: To solve this problem, we first leave 5/2 alone so don't do anything to it.
For our second fraction, we want to switch the numerator and the
denominator which means find the reciprocal of it.
The reciprocal of 2/5 is just the opposite of it when
you flip it and it's going to be 5/2.
Because we did the opposite there, we need to do the opposite
of division and the opposite of division is multiplication.
So now we have 5/2 × 5/2 which is 25/4 or 6 and 1/4.
Answer:
4 units to the left
Step-by-step explanation:
y = a (x - h)² + k
The h is a horizontal translation of <em>h</em> units.
For h > 0, move right
For h < 0, move left
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