Question

if the population of a a society of bacteria doubles evry 45 min. how would you write the equation for the number of bacteria, A, after t minutes, given an initial number of a0 bacteria.

Answer 1

\[A=A_0\times 2^{\frac{t}{45}}\]

Answer 2

oh and if the bacteria was 1500 in how many minutes will the population appro reach 35000? answer to the nearest minute . show work please

Answer 3

if the intial number of bacteria was 1500.

Answer 4

solve
\[35000=1500\times 2^{\frac{t}{45}}\] for t. first divide by 1500 to get
\[\frac{7}{3}=2^{\frac{t}{45}}\] then
\[\frac{t}{45}=\frac{\ln(\frac{7}{3})}{\ln(2)}\] and finally
\[t=\frac{45\ln(\frac{7}{3})}{\ln(2)}\]

Answer 5

oh and how would you do this question: \[\log_{8} (x+1)=1-\log_{8} (x+8)\]