Answer:
[tex]y = 100 * (0.75)^{30[/tex]
Step-by-step explanation:
Given
[tex]a =100[/tex] --- Initial Amount
[tex]r= 25\%[/tex] every 10 years
Required
The remaining amount after 300 years
To do this, we make use of:
[tex]y = a(1 - r)^T[/tex]
Where
r = decay rate
T = the period of decay
In 300 years, there are 30 periods of 10 years.
i.e.
[tex]T = \frac{300}{10}[/tex]
[tex]T = 30[/tex]
[tex]y = a(1 - r)^T[/tex]
[tex]y = 100 * (1 - 25\%)^{30[/tex]
[tex]y = 100 * (1 - 0.25)^{30[/tex]
[tex]y = 100 * (0.75)^{30[/tex]
