MHB Calculating Time for Iodine 131 to Decay to 5% of Initial Dose

[Pikachu1]

So i have a graph representing iodine 131
y axis of 0-100 iodine remaining in the body (%of dose)
x asis 0-60 Time in days
with the points plotted (24,12.5)

The equation of the graph is D = D0 (b) t/k

So i have figured out "k" which is 8 for iodine half life. Which it asked me to do in the previous question.

Now it is asking me...

Iodine 131 is unable to be detected after it has decayed to 5% of its initial dose. Using your equation, determine how many days, to the nearest tenth will have passed until the dose is undetectable.

Just not sure how to use my equation to get that answer. I realize it's simple but it is out smarting me.

 

[MarkFL]

Okay the curve is:

$$D(t)=D_02^{-\frac{t}{8}}$$

To find the time at which the initial dose has decayed to 5% of the original amount, you may set $D(t)=0.05D_0$ and then solve for $t$. Can you proceed?