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Fudgin [204]
3 years ago
13

A certain type of bacteria is growing at an exponential rate that is modeled by the equation y= ae^kt, where t represents the nu

mber of hours. There are 100 bacteria initially, and 500 bacteria five hours later.
Mathematics
1 answer:
eimsori [14]3 years ago
5 0

Answer:

The number of bacteria after t hours is given by: y(t) = 100e^{0.3219t}

Step-by-step explanation:

Amount of bacteria after t hours:

Is given by the following equation:

y(t) = ae^{kt}

In which a is the initial value and k is the constant of growth.

There are 100 bacteria initially

This means that a = 100. So

y(t) = ae^{kt}

y(t) = 100e^{kt}

500 bacteria five hours later.

This means that y(5) = 500. We use this to find k. So

y(t) = 100e^{kt}

500 = 100e^{5k}

e^{5k} = 5

\ln{e^{5k}} = \ln{5}

5k = \ln{5}

k = \frac{\ln{5}}{5}

k = 0.3219

So

y(t) = 100e^{kt}

y(t) = 100e^{0.3219t}

The number of bacteria after t hours is given by: y(t) = 100e^{0.3219t}

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