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Sagot :
Growth of Culture of bacteria increases in number according to the formula :
[tex]N(t)=45(1.85)^t[/tex]N = Number of bacteria present
t = number of hours from the initial state.
a) number of bacteria at the start of the experiment.
In the begining when the expreiment start, the time is zero
t = 0
Substitute t = 0 in the growth expression of bacteria
[tex]\begin{gathered} N(t)=45(1.85)^t \\ N(0)=45(1.85)^0 \\ as\colon a^0=1 \\ N(0)=45(1) \\ N(0)=45 \end{gathered}[/tex]When the experiment start, number of bacteria is 45
b) number of bacteria present after 4 hours, giving your answer to the nearest whole number of bacteria.
After fours hours, i.e. t = 4
Substitute t = 4 in the growth expression of bacteria
[tex]\begin{gathered} N(t)=45(1.85)^t \\ N(4)=45(1.85)^4 \\ N(4)=45\times11.7135 \\ N(4)=527.1077 \\ N(4)=527 \end{gathered}[/tex]Number of bacteria after 4 hours are 527
c) the time it would take for the number of bacteria to reach 1000.
Here, we have number of bacteria 1000 i.e. N = 1000
Substitute the value and solve for t:
[tex]\begin{gathered} N(t)=45(1.85)^t \\ 1000=45(1.85)^t \\ \frac{1000}{45}=1.85^t \\ 1.85^t=\frac{200}{9} \\ 1.85^t=22.22 \\ \text{Taking log on both side: } \\ t\ln (1.85)=\ln (22.22) \\ t=\frac{\ln (22.22)}{\ln (1.85)} \\ t=5.0409 \\ t=5 \end{gathered}[/tex]It will take 5 years to reach upto 1000 bacteria
Answer:
a) Number of bacteria at the start of experiment 45
b) Number of bacteria after 4 hours 527
c) It would take 5 years to reach upto 1000 bacteria
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