Answer :
Answer:
Approximately 1,933.64 years, it will take until 50 ounce of this substance remains.
Step-by-step explanation:
Given that,
The amount, in ounce, of the substance that is left after t years can be modeled by the equation
[tex]y=2000e^{-0.00043t}[/tex]
To find the time, we put y = 50 ounce in the above equation.
[tex]50=2000e^{-0.00043t}[/tex]
[tex]\Rightarrow\frac{ 50}{2000}=e^{-0.00043t}[/tex]
[tex]\Rightarrow\frac{ 1}{400}=e^{-0.00043t}[/tex]
Taking ln function both sides of the above equation
[tex]\Rightarrow ln|\frac{ 1}{400}|=ln|e^{-0.00043t}|[/tex]
[tex]\Rightarrow ln|{ 1}|-ln|{400}|=ln|e^{-0.00043t}|[/tex] [ since [tex]ln| \frac ab|= ln|a|- ln| b|[/tex] ]
[tex]\Rightarrow -ln|{400}|={-0.00043t}[/tex] [ since [tex]ln|1|=0[/tex] and [tex]e^{ln |a|}=a[/tex] ]
[tex]\Rightarrow t = \frac{ln|{400}|}{0.00043}[/tex]
≈1,933.64 years.
Approximately 1,933.64 years, it will take until 50 ounce of this substance remains.