Question

assignment overview 9 deltamath
score: 1/3 penalty: none
half life and doubling time
question video examples
in a lab experiment, 60 bacteria are
placed in a petri dish. the conditions
are such that the number of bacteria is
able to double every 12 hours. how
many bacteria would there be after 16
hours, to the nearest whole number?
answer
attempt 1 out of 2

Explanation:

Step1: Write the exponential growth formula

The formula for exponential growth is \(N = N_0\times2^{\frac{t}{d}}\), where \(N_0\) is the initial amount, \(t\) is the time passed, and \(d\) is the doubling - time. Here, \(N_0 = 60\), \(t = 16\) hours, and \(d=12\) hours.

Step2: Substitute the values into the formula

Substitute the values into the formula: \(N = 60\times2^{\frac{16}{12}}\). Simplify the exponent \(\frac{16}{12}=\frac{4}{3}\). So, \(N = 60\times2^{\frac{4}{3}}\).

Step3: Calculate \(2^{\frac{4}{3}}\)

We know that \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\). So, \(2^{\frac{4}{3}}=\sqrt[3]{2^{4}}=\sqrt[3]{16}\approx2.5198\).

Step4: Calculate the value of \(N\)

Multiply 60 by \(2.5198\): \(N = 60\times2.5198 = 151.188\).

Answer:

\(151\)