Answer:
[tex]a.A_t=A_o.(\frac{1}{2})^t^/^{t_h}[/tex]
[tex]b. 0.010986grams[/tex]
[tex]c.109.84 mins[/tex]
Step-by-step explanation:
Let [tex]t_1_/_2[/tex] denote the half life of our substance [tex]t[/tex] to be our time, [tex]A_t[/tex] is mass at time t and [tex]A_o[/tex] as initial mass. Our half life equation can be expressed as:
[tex]A_t=A_o.(\frac{1}{2})^t^/^{t_h}[/tex] from which we can obtained mass at any given time.
b. From our equation above,
we can convert our t into mins as [tex]t=4*60=240mins[/tex]
We then substitute [tex]t[/tex] value into the equation
[tex]A_2_4_0=45\times(1/2)^2^4^0^/^2^0\\=0.010986\\=0.010986grams[/tex]
Hence mass after 4hrs is [tex]0.010986grams[/tex]
c. We can set our final mass to [tex]1g[/tex] then substitute in the equation
[tex]A_t=A_o.(\frac{1}{2})^t^/^{t_h}[/tex]. Substitute [tex]A_t=1g[/tex]
[tex]1.0=45\times(1/2)^t^/^20[/tex]
[tex]1.0=45\times(1/2)^t^/^2^0\\log(1/45)=(t/20)\times log(1/2)\\t=20\times5.491853=109.84 mins[/tex]
Hence time until [tex]1g[/tex] mass is 109.83 minutes
