The number of bacteria y (in thousands) in a culture can be approximated by the model y=100(1.99)^t, where t I’d the number of hours the culture is incubated.

Estimate when the number of bacteria will be 1,000,000.

Please help!

Recall that "y"in the equation is the number of individuals at time "t"; 100 is the starting number of the initial population, and t represents the elapsed time (in hours). So "t" i our unknown, and we know all the other values. Since "t" is in the exponent, we proceed to: first isolate the exponential expression, and second, to bring that unknown exponent "t" down by the use of logarithms.

[tex]y=100\,(1.99)^t\\1000000=100\,(1.99)^t\\\frac{1000000}{100} = (1.99)^t\\10000=(1.99)^t\\log(10000)=t*log(1.99)\\4=t*log(1.99)\\t=\frac{4}{log(1.99)} \\t=13.3845\, hours[/tex]

The number of bacteria y (in thousands) in a culture can be approximated by the model y=100(1.99)^t, where t I’d the number of hours the culture is incubated. Estimate when the number of bacteria will be 1,000,000. Please help!

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The number of bacteria y (in thousands) in a culture can be approximated by the model y=100(1.99)^t, where t I’d the number of hours the culture is incubated.

Estimate when the number of bacteria will be 1,000,000.

Please help!