Answer: [tex]t=\dfrac{\ln(4.09)}{3}[/tex]
Step-by-step explanation:
Given function: [tex]y(t)=35e^{3t}+57[/tex] which represents the number of bacteria present at time t minutes.
Put y(t) = 200 in the above equation , we get
[tex]200=35e^{3t}+57\\\\\Rightarrow\ 35e^{3t}=143\\\\\Rightarrow\ e^{3t}=4.085714285\approx4.09[/tex]
Taking log on both sides, we get
[tex]\ln(e^{3t})=\ln(4.09)\\\\\Rightarrow\ 3t=\ln(4.09)\\\\\Rightarrow\ t=\dfrac{\ln(4.09)}{3}[/tex]
Hence, the the population reach 200 bacteria at [tex]t=\dfrac{\ln(4.09)}{3}[/tex] minutes.
At [tex]t =\frac{1}{3} ln\frac{143}{35}[/tex], the population of bacteria will be 200.
Given function is
[tex]y(t) = 35e^{3t} +57[/tex]...........(1)
Where y(t) is the number of bacteria at time t.
A function of form y =a^x + b is called exponential function, where a≠1.
We have to find a time t when the population of bacteria will be 200.
i.e. y(t) = 200
Put y(t) = 200 in (1)
We have,
[tex]200= 35e^{3t} +57\\200-57 = 35e^{3t}\\143 = 35e^{3t} \\takeLOGbothsides\\ln 143 = ln35+3t\\t = \frac{1}{3} ln\frac{143}{35}[/tex]
Therefore, At [tex]t =\frac{1}{3} ln\frac{143}{35}[/tex], the population of bacteria will be 200.
To get more about exponential function visit:
https://brainly.com/question/2456547
