Question

COLLEGE ALGEBRA!!!!

Answer 1

Answer:

$a.A_t=A_o.(\frac{1}{2})^t^/^{t_h}$

$b. 0.010986grams$

$c.109.84 mins$

Step-by-step explanation:

Let  $t_1_/_2$ denote the half life of our substance $t$ to be our time, $A_t$ is mass at time t and $A_o$ as initial mass. Our half life equation can be expressed as:

$A_t=A_o.(\frac{1}{2})^t^/^{t_h}$ from which we can obtained mass at any given time.

b. From our equation above,

we can convert our t into mins as $t=4*60=240mins$

We then substitute $t$ value into the equation

$A_2_4_0=45\times(1/2)^2^4^0^/^2^0\\=0.010986\\=0.010986grams$

Hence mass after 4hrs is $0.010986grams$

c. We can set our final mass to $1g$  then substitute in the equation

$A_t=A_o.(\frac{1}{2})^t^/^{t_h}$. Substitute $A_t=1g$

$1.0=45\times(1/2)^t^/^20$

$1.0=45\times(1/2)^t^/^2^0\\log(1/45)=(t/20)\times log(1/2)\\t=20\times5.491853=109.84 mins$

Hence time until $1g$ mass is 109.83 minutes