Question

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 8.3%
How many hours does it take for the size of the sample to double?
Note: This is a continuous exponential growth model.
Do not round any intermediate computations, and round your answer to the nearest hundredth.​

Answer 1

It takes 8.35 hours for the size of the sample to double

Step-by-step explanation:

The form of the continuous exponential growth model is

$A=Pe^{rt}$ , where

• A is the new value
• P is the initial value
• r is the rate of growth or decay  in decimal
• t is the time

∵ The growth rate is 8.3%

∴ r = 8.3 ÷ 100 = 0.083

∵ The size of the sample will doubled in t hours

∴ A = 2 P

Use the formula of the contentious exponential growth above

∵ $2P=Pe^{0.083t}$

- Divide both sides by P

∴ $2=e^{0.083t}$

- Insert ㏑ in both sides

∴ $ln(2)=ln(e^{0.083t})$

- Remember $ln(e^{n})=n$ because ㏑(e) = 1

∴ $ln(2)=0.083t$

- Divide both sides by 0.083

∴ $\frac{ln(2)}{0.083}=t$

∴ t = 8.35 hours to the nearest hundredth

It takes 8.35 hours for the size of the sample to double

Learn more:

You can learn more about the logarithmic function in brainly.com/question/1447265

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