Respuesta :
The linear equation that could model the decreasing yearly supply of helium due to human consumption is [tex]m(t) = 35\times 10^{9} -210\times 10^{6}\cdot (t-2018)[/tex], where [tex]t[/tex] is the year, no unit, and [tex]m(t)[/tex] is the volume of helium remaining, in cubic meters.
In this question we know the world reserves of helium and the rate of consumption for every year. Given that rate of consumption is constant in time, then we can use the following linear function to model consumption:
[tex]m (t) = m_{o} - \dot m \cdot (t-t_{o})[/tex] (1)
Where:
- [tex]m_{o}[/tex] - Initial supply of helium, in cubic meters.
- [tex]\dot m[/tex] - Consumption rate, in cubic meters per year.
- [tex]t_{o}[/tex] - Initial year, no unit.
- [tex]t[/tex] - Current year, no unit.
If we know that [tex]m_{o} = 35\times 10^{9}\,m^{3}[/tex], [tex]\dot m = 210\times 10^{6}\,m^{3}[/tex] and [tex]t_{o} = 2018[/tex], then the linear equation that represents the decreasing supply of helium is:
[tex]m(t) = 35\times 10^{9} -210\times 10^{6}\cdot (t-2018)[/tex] (2)
Hence, the linear equation that represents the decreasing supply of helium is [tex]m(t) = 35\times 10^{9} -210\times 10^{6}\cdot (t-2018)[/tex].
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Helium is being used for the production of fiber optic as well as semiconductors and for arc soldering to have an inert protective atmosphere. This is also used in the detection of leaks, for example to car air conditioners.
In this, linear equation the model decreasing annual helium supply by human use is [tex]\bold{m(t)=35 \times 10^9-210 \times 10^6 \cdot (t-2018) }[/tex], where [tex]\bold{ t }[/tex] is just a given year, no unit, and [tex]\bold{m(t)}[/tex] in cubic metres.
We know the global helium reserves and the annual consumption rate in this question.
Since the consumer rate is consistent in time, the following linear model can be used to model consumption:
[tex]\to \bold{m(t)=m_o-m\cdot (t-t_o)}.............(1)[/tex]
Where:
[tex]m_o \to[/tex] Helium supply in the cubic meters at the beginning.
[tex]m \to[/tex] Consumption rate, per year in cubic meters.
[tex]t_o \to[/tex] No unit in the first year.
[tex]t \to[/tex] No unit this year.
If indeed the equation representing this same reducing supply of hydrogen seems to be:
if we are aware that [tex]\to \bold{m_o=35 \times 10^9 m^3, m=210 \times 10^6 m^3, \ and\ t_o=2018 }[/tex]
[tex]\to \bold{m(t)=35 \times 10^9-210 \times 10^6 \cdot (t-2018).............. (2)}[/tex]
Thus, the linear equation of the lower helium supply is:
[tex]\bold{ m(t)=35 \times 10^9-210 \times 10^6 \cdot (t-2018)}[/tex]
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