Answer:
16.34 hours
Step-by-step explanation:
According to the given information we can see that the case is of exponential growth
Hence, we will use the formula
[tex]A=P(2)^\frac{t}{24}[/tex]
Here A =800 is the amount that is needed to reach
P is the initial amount that is 500
We have to find the time it will take to reach 800 that is we need to find t
On substituting the values in the formula we get
[tex]800=500(2)^\frac{t}{24}[/tex]
On simplification we get
[tex]\Rightarrow\frac{8}{5}=(2)^\frac{t}{24}[/tex]
Taking log on both sides we get
[tex]\Rightarrow\log\frac{8}{5}=\log(2)^\frac{t}{24}[/tex]
using [tex]\log\frac{m}{n}=\log m-\log n[/tex]
And [tex]\log a^m=m\log a[/tex]
[tex]\Rightarrow\log{8}-\log{5}=\frac{t}{24}\log2[/tex]
Now substituting values of log 8=0.903, log 5=0.698 and log 2=0.301 we get
[tex]\Rightarrow 0.903-0.698=\frac{t}{24}0.301[/tex]
[tex]\Rightarrow 0.205=\frac{t}{24}0.301[/tex]
[tex]\Rightarrow \frac{0.205}{0.301}\cdot 24=t[/tex]
[tex]\Rightarrow t=16.34[/tex]
