The answer is 28 years
At = A0 * e^(-k * t)
At = 12 g
A0 = 15 g
k = 7.9 × 10^-3 = 0.0079
t = ?
12 = 15 * e^(-0.0079 * t)
12/15 = e^(-0.0079 * t)
0.8 = e^(-0.0079 * t)
Logarithm both sides (because ln(e) = 1:
ln(0.8) = ln(e^(-0.0079 * t))
ln(0.8) = (-0.0079 * t) * ln(e)
-0.223 = -0.0079 * t
t = -0.223 / -0.0079
t = 28.23
t ≈ 28 years
0.77 is the answer to your question
Answer:
im assuming you need the volume of this container:
Step-by-step explanation:
We find the stationary point of (20 + 2x)(1200 - 60x),
where x is the unit rate of increase/decrease.
d/dx [(20 + 2x)(1200 - 60x)]
= d/dx (-120x² + 1200x + 24000)
= -240x + 1200.
When d/dx [(20 + 2x)(1200 - 60x)] = 0,
We have -240x + 1200 = 0. => x = 5.
Price per shirt that maximise revenue
= $20 + $2x = $20 + $2(5) = $30.
Maximum revenue
= (20 + 2(5))(1200 - 60(5))
= $30 * 900 = $27,000.
This question involves a system of equations.
for the variables we will use c for computer, p for printer, and s for scanner.
in order to solve a system of equations, we need to solve one variable, so we will just pick c because we are solving for the computer.
when we set up the
equation, we need to convert all the variables into an applicable form of c, since that is the variable we are solving for. we can do this because we have information on how the other variables differ on c.
so we get these translations:
c = c
p = c - 1502
s = p - 123
however, the scanner is not translated to c yet, it is translated into p, but we know p can translate into c, so we plug in the equation for p as so:
s = (c - 1502) - 123
which translates to
s = c - 1625
now we have
c = c
p = c - 1502
s = c - 1625
now that we have the translations, we have to use the original equation given to us which is
c + p + s = 2543
which, with our translations can be said as
c + (c - 1502) + (c - 1625) = 2543
which simplifies to
3c - 3127 = 2543.
now, we add 3127 to both sides to get
3c = 5670
then, we divide 3 to both sides to get
c = 1890
so the computer costs 1890.
if you want to find the price for the printer and scanner, simply take c and plug it in to the other equations as so.
p = 1890 - 1502 (388)
s = 1890 - 1625 (265)
