a culture started with 2,000 bacteria. After 4 hours, it grew to 2,200 bacteria. Predict how many bacteria will be present in 9 hours. round your answer to the nearest whole number... exponential growth formula
Well, the starting value (N0 in my notation, A in yours) is 2000. This is the value at time t = 0.
At time t = 4 the value of N (my notation) or P (your notation) is 2200.
So at time t = 4 we have 2200 = 2000*ek*4
Divide both sides by 2000
2200/2000 = ek*4
or 1.1 = ek*4
Now take logs of both sides:
ln(1.1) = ln(ek*4)
or ln(1.1) = k*4 (because ln(ex) = x)
Divide both sides by 4
ln(1.1)/4 = k
$${\mathtt{k}} = {\frac{{ln}{\left({\mathtt{1.1}}\right)}}{{\mathtt{4}}}} \Rightarrow {\mathtt{k}} = {\mathtt{0.023\: \!827\: \!544\: \!951\: \!081\: \!2}}$$
Now use this value of k to find N (my notation) or P (your notation) at time t = 9
P = 2000*e0.023827544951*9
$${\mathtt{P}} = {\mathtt{2\,000}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{\left({\mathtt{0.023\: \!827\: \!544\: \!951}}{\mathtt{\,\times\,}}{\mathtt{9}}\right)} \Rightarrow {\mathtt{P}} = {\mathtt{2\,478.355\: \!127\: \!582\: \!545\: \!6}}$$
or P ≈ 2478
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Have a look at the answer here: http://web2.0calc.com/questions/a-countrys-population-in-1995-was-56-million-in-2002-it-was-59-million-estimate-the-population-in-2016-using-exponential-growth-formula-roun and use the same method.
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The exponential growth equation is N=N0ekt
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Your expression is mathematically the same as mine Anonymous. You've just used different symbols!
o okay but i still dont understand even after reading the other answer to the question
Well, the starting value (N0 in my notation, A in yours) is 2000. This is the value at time t = 0.
At time t = 4 the value of N (my notation) or P (your notation) is 2200.
So at time t = 4 we have 2200 = 2000*ek*4
Divide both sides by 2000
2200/2000 = ek*4
or 1.1 = ek*4
Now take logs of both sides:
ln(1.1) = ln(ek*4)
or ln(1.1) = k*4 (because ln(ex) = x)
Divide both sides by 4
ln(1.1)/4 = k
$${\mathtt{k}} = {\frac{{ln}{\left({\mathtt{1.1}}\right)}}{{\mathtt{4}}}} \Rightarrow {\mathtt{k}} = {\mathtt{0.023\: \!827\: \!544\: \!951\: \!081\: \!2}}$$
Now use this value of k to find N (my notation) or P (your notation) at time t = 9
P = 2000*e0.023827544951*9
$${\mathtt{P}} = {\mathtt{2\,000}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{\left({\mathtt{0.023\: \!827\: \!544\: \!951}}{\mathtt{\,\times\,}}{\mathtt{9}}\right)} \Rightarrow {\mathtt{P}} = {\mathtt{2\,478.355\: \!127\: \!582\: \!545\: \!6}}$$
or P ≈ 2478
.