Question 1189594
the formula is y = x * e ^ (r * t)
to find the doubling time, let x = 1 and y = 2 and t = 23 days.
the formula becomes:
2 = 1 * e ^ (r * 23)
take the natural log of both sides of the equation to get:
ln(2) = ln(1 * e ^ (r * 23)
since 1 * e = e, the formula becomes:
ln(2) = ln(e ^ (r * 23)
since ln(e ^ (r * 23) = r * 23 * ln(e) and since ln(3) = 1, the formula becomes:
ln(2) = r * 23
divide both sides of the equation by 23 to get:
ln(2) / 23 = r
solve for r to get:
r = .0301368339.
solve for y in the formula to confirm the dobuling time is correct.
you get:
y = 1 * e ^ (.0301368339 * 23) = 2.
this confirms the doubling time is correct.
when the starting value is 72.6, the doubling time will be:
y = 72.6 * e ^ (.0301368339 * 23) = 145.2
since 145.2 is double 72.6, the doubling time is correct when the initial value is 72.6.
when the time from inception if 8 days, then the formula becomes:
y = 72.6 * e ^ (.0301368339 * 8) = 92.39377381.
round this to the nearest 10th to get 92.4
that's your solution.
the formula can be graphed by letting x = t.
here's what the graph looks like.


<img src = "http://theo.x10hosting.com/2022/011301.jpg" >