Answer:
total time = 304.21 s
Explanation:
given data
y = 50% = 0.5
n = 1.1
t = 114 s
y = 1 - exp(-kt^n)
solution
first we get here k value by given equation
y = 1 - [tex]e^{(-kt^n)}[/tex] ...........1
put here value and we get
0.5 = 1 - e^{(-k(114)^{1.1})}
solve it we get
k = 0.003786 = 37.86 × [tex]10^{4}[/tex]
so here
y = 1 - [tex]e^{(-kt^n)}[/tex]
1 - y = [tex]e^{(-kt^n)}[/tex]
take ln both side
ln(1-y) = -k × [tex]t^n[/tex]
so
t = [tex]\sqrt[n]{-\frac{ln(1-y)}{k}}[/tex] .............2
now we will put the value of y = 87% in equation with k and find out t
t = [tex]\sqrt[1.1]{-\frac{ln(1-0.87)}{37.86*10^{-4}}}[/tex]
total time = 304.21 s
