suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1700 bacteria selected from this population reach the size of 1892 bacteria in three hours. Find the hourly growth rate parameter

Question

Mathematics

Perkins

6 February, 17:45

suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1700 bacteria selected from this population reach the size of 1892 bacteria in three hours. Find the hourly growth rate parameter

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Jennifer Price · Answer 1

3.33% per hour

Step-by-step explanation:

Use the A=Pe^rt equation. A is the end amount, so it's 1892. P is the original amount, 1700. E is a constant, around 2.72. R is the growth constant. T is the time that passed, 3 hours. You can substitute the givens into the equation and get 1892=1700e^ (3r). Divide by 1700 to isolate the e. This leaves you with 1892/1700=e^ (3r). Do the natural log of each side cancel the e and bring the exponent down. This leaves you with ln (1892/1700) = 3r. Divide by 3 to isolate r. ln (1892/1700) is. 1 ...1/3 is. 03333. Multiply by 100 to get a percent. 3.33 percent is your final answer.