(a) Show that if a quantity y = y(t) has an exponentialmodel, and if y(t1) = y1 and
Chapter 8, Problem 45(choose chapter or problem)
(a) Show that if a quantity \(y=y(t)\) has an exponential model, and if \(y\left(t_{1}\right)=y_{1}\) and \(y\left(t_{2}\right)=y_{2}\), then the doubling time or the half-life T is
\(T=\left|\frac{\left(t_{2}-t_{1}\right) \ln 2}{\ln \left(y_{2} / y_{1}\right)}\right|\)
(b) In a certain 1-hour period the number of bacteria in a colony increases by \(25 \%\). Assuming an exponential growth model, what is the doubling time for the colony?
Equation Transcription:
Text Transcription:
y=y(t)
y(t_1)=y_1
y(t_2)=y_2
T=|(t_2-t_1)ln 2/ln(y_2/y_1)|
25%
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