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The initial number of bacteria in the dish was 1,150. The amount of bacteria doubles at the end of each hour. Write a function b(t) that would represent this relationship after t hours. Use this function to determine how many bacteria would be in the dish after 10 hours and write it only as a number without units.

User Whypee
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1 Answer

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Answer:


B(t) = 1150*(2)^(t)

After 10 hours: 1,177,600

Explanation:

The number of bacteria after b hours is given by the following equation:


B(t) = B(0)(1+r)^(t)

In which B(0) is the initial number of bacteria and r is the rate that it increases.

The initial number of bacteria in the dish was 1,150. The amount of bacteria doubles at the end of each hour.

This means that
B(0) = 1150, B(1) = 2*1150

So


B(t) = B(0)(1+r)^(t)


2*1150 = 1150(1+r)^(1)


1 + r = 2


r = 1

So


B(t) = 1150*(2)^(t)

After 10 hours:


B(10) = 1150*(2)^(10) = 1177600

1,177,600 bacteria after 10 hours.

User DennisVA
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