Answer:
The time to reach 1000 mg is 7 hours
Step-by-step explanation:
Given as :
The rate at which bacteria growing = 2.34% per hour
The initial amount of bacteria = 850 mg
The final amount of bacteria = 1000 mg
Let The time period fro bacteria growing = T hours
Now, Final value = Initial value × [tex](1 + \frac{Rate}{100})^{Time}[/tex]
Or, 1000 mg = 850 mg × [tex](1 + \frac{2.34}{100})^{T}[/tex]
Or, [tex]\frac{1000}{850}[/tex] = [tex](1 + \frac{2.34}{100})^{T}[/tex]
Or, 1.1764 = [tex](1 + \frac{2.34}{100})^{T}[/tex]
Or, 1.1764 = [tex](1.0234)^{T}[/tex]
Or, Taking log both side
log(1.1764) = log ( [tex](1.0234)^{T}[/tex] )
Or, 0.07055 = T × 0.01004 ( [tex]loga^{b} = b log a[/tex])
∴ T = 7.026 hour or T ≈ 7 hours
Hence The time to reach 1000 mg is 7 hours Answer
