# Updating half life

You can click the arrows to change the scales of the graph. For example, we fit a linear discrete dynamical system model to the population growth of the bacteria V. The resulting exponential growth equation was $P_T = 0.022 \times 1.032^T$ (equation (6) of the bacteria growth page.) We can plot the V.natriegens along with the model function in a modified version of the above applet. The previous applet shown with data from the population growth of the bacteria V. For the model $P_T = 0.022 \times 1.032^T$ fit to the data, the doubling time is about 22 minutes. Observe that at $T = 26$, $P = 0.05$ and at $T=48$, $P = 0.1$; thus $P$ doubled from 0.05 to 0.1 in the 22 minutes between $T=26$ and $T=48$.We'll show that this $T_$ won't depend on our choice of $t_1$.To determine $t_2$ (and hence $T_$), we must solve the equation \begin x_ = 2 x_ \end which, according to the model of equation \eqref, we can rewrite as \begin x_0 \times b^ = 2 x_0 \times b^.

For example, for the model $P_t = 0.4 \times 0.82^t$, you will find that the half-life is about 3.5.

Sometimes, a population size $P_T$ as a function of time can be characterized by an exponential function.

For example, the population growth of bacteria was characterized by the function $P_T = 0.022 \times 1.032^T$.

For the equation, $P_T = 0.022 \times 1.032^T$, the doubling time is $\log 2 / \log 1.032 = 22.0056$, as shown in the above applet.

For the exponential equation $y_t = y_0 \times b^t$ with

For example, for the model $P_t = 0.4 \times 0.82^t$, you will find that the half-life is about 3.5.Sometimes, a population size $P_T$ as a function of time can be characterized by an exponential function.For example, the population growth of bacteria was characterized by the function $P_T = 0.022 \times 1.032^T$.For the equation, $P_T = 0.022 \times 1.032^T$, the doubling time is $\log 2 / \log 1.032 = 22.0056$, as shown in the above applet.For the exponential equation $y_t = y_0 \times b^t$ with [[

For example, for the model $P_t = 0.4 \times 0.82^t$, you will find that the half-life is about 3.5.

Sometimes, a population size $P_T$ as a function of time can be characterized by an exponential function.

For example, the population growth of bacteria was characterized by the function $P_T = 0.022 \times 1.032^T$.

For the equation, $P_T = 0.022 \times 1.032^T$, the doubling time is $\log 2 / \log 1.032 = 22.0056$, as shown in the above applet.

For the exponential equation $y_t = y_0 \times b^t$ with $0 \lt b \lt 1$, the quantity $y_t$ does not grow with time $t$. The half-life, $T_$ is the time it takes for $y_t$ to decrease by one-half.

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For example, for the model $P_t = 0.4 \times 0.82^t$, you will find that the half-life is about 3.5.Sometimes, a population size $P_T$ as a function of time can be characterized by an exponential function.For example, the population growth of bacteria was characterized by the function $P_T = 0.022 \times 1.032^T$.For the equation, $P_T = 0.022 \times 1.032^T$, the doubling time is $\log 2 / \log 1.032 = 22.0056$, as shown in the above applet.For the exponential equation $y_t = y_0 \times b^t$ with $0 \lt b \lt 1$, the quantity $y_t$ does not grow with time $t$. The half-life, $T_$ is the time it takes for $y_t$ to decrease by one-half.

]] \lt b \lt 1$, the quantity$y_t$does not grow with time$t$. The half-life,$T_$is the time it takes for$y_t$to decrease by one-half. \lt b \lt 1$, the quantity $y_t$ does not grow with time $t$. The half-life, $T_$ is the time it takes for $y_t$ to decrease by one-half.

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