Mathematics: Choose all the expressions that show this statement is true.

If is the amount of oil in the well (let s say in millions of barrels) at time for some negative value of . You re told that the well started off with 3 million barrels, so , and that after 6 years, there are 1.5 million barrels, so .Solve the differential equation above:Integrate both sides.Given that and , you haveSo the amount of oil in the well is given by the function...

Choose all the expressions that show this statement

Ответ:

Deuce9024

24.06.2021

Mathematics

F. or C.

Step-by-step explanation:

0,0(0 оценок)

Ответ:

Kyliehayden05

07.04.2023

Mathematics

is the amount of oil in the well (let's say in millions of barrels) at time $t[tex] (years), then\\[tex]\dfrac{\mathrm dA}{\mathrm dt}=kA$

for some negative value of

. You're told that the well started off with 3 million barrels, so A(0)=3

, and that after 6 years, there are 1.5 million barrels, so A(6)=1.5

.

Solve the differential equation above:

$\dfrac{\mathrm dA}{\mathrm dt}=kA\implies\dfrac{\mathrm dA}A=k\,\mathrm dt$

Integrate both sides.

$\displaystyle\int\frac{\mathrm dA}A=k\int\mathrm dt$
$\ln|A|=kt+C$
$A=e^{kt+C}$
$A=Ce^{kt}$

Given that A(0)=3

and

, you have

$\begin{cases}3=Ce^{0k}\\1.5=Ce^{6k}\end{cases}\implies C=3,\,k=-\dfrac{\ln2}6$

So the amount of oil in the well is given by the function

$A(t)=3e^{-\frac{\ln2}6t}=3\times2^{-t/6}$

0,0(0 оценок)

Choose all the expressions that show this statement is true.

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question