Answer:
[tex]\boxed{\text{75.5 g}}[/tex]
Step-by-step explanation:
The amount of substance decreases by 50 % every half-life.
Thus, 50 % of the substance remains at the end of each half-life.
The exponential function is
[tex]a = a_{0}\left( \dfrac{1}{2}\right)^{x}[/tex]
where x = the number of half-lives.
Data:
a₀ = 265 g
[tex]t_{\frac{1}{2}} = \text{138 da}[/tex]
t = 250 da
Calculations:
(a) Calculate x
[tex]x = \dfrac{250}{138} \approx 1.812[/tex]
(b) Calculate a
[tex]a = 265\left( \dfrac{1}{2}\right)^{1.812}\\\\a = 265 \times 0.2849 = \boxed{\textbf{75.5 g}}[/tex]
