In a lab experiment, 80 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 16 hours. Write a function showing the number of bacteria after tt hours, where the hourly growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per hour, to the nearest hundredth of a percent.

Answer:

The hourly growth rate is of 4.43%.

The function showing the number of bacteria after t hours is [tex]P(t) = 80(1.0443)^t[/tex]

Step-by-step explanation:

Equation of population growth:

The equation for the population after t hours is given by:

[tex]P(t) = P(0)(1+r)^t[/tex]

In which P(0) is the initial population and r is the growth rate, as a decimal.

The conditions are such that the number of bacteria is able to double every 16 hours.

This means that [tex]P(16) = 2P(0)[/tex]. We use this to find r.

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]2P(0) = P(0)(1+r)^{16}[/tex]

[tex](1+r)^{16} = 2[/tex]

[tex]\sqrt[16]{(1+r)^{16}} = \sqrt[16]{2}[/tex]

[tex]1 + r = 2^{\frac{1}{16}}[/tex]

[tex]1 + r = 1.0443[/tex]

[tex]r = 1.0443 - 1[/tex]

[tex]r = 0.0443[/tex]

The hourly growth rate is of 4.43%.

80 bacteria are placed in a petri dish.

This means that [tex]P(0) = 80[/tex].

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]P(t) = 80(1+0.0443)^t[/tex]

[tex]P(t) = 80(1.0443)^t[/tex]

The function showing the number of bacteria after t hours is [tex]P(t) = 80(1.0443)^t[/tex]

PLEASE HALP MAH! The dot plots below show the test scores of some mathematics students and some science students: Two dot plots are shown one below the other. The top and the bottom plots have the title Mathematics Students and Science Students respectively. Below the line for each dot plot is written Mark. The markings on each line are from 30 to 50 at intervals of 1. For the top plot there are two dots each for 34 and 40 and 1 dot each for 32, 33, 35, 37, and 39. For the bottom plot there are 2 dots each for 43, 46 and 49 and 1 dot each for 41, 42, and 47. Based on visual inspection of the dot plots, which group of students appears to have the larger average score? The mathematics students The science students Both groups are similar. Not enough information is available to draw a conclusion.

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