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Dr. Jimenez found that after applying an antibiotic to bacteria, he observed only 90% of the bacteria left in the culture dish each hour. If the initial bacteria count was 100, what was the bacteria count after 5 hours? Round to the nearest whole number.

There were ___ bacteria after 5 hours.

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bandzlvr
Answer:
There were 59 bacteria after 5 hours.
MrRoyal

The complete statement is:

There were 59 bacteria after 5 hours

The initial population of the bacteria is given as:

[tex]a =100[/tex]

The proportion left after each hour is given as:

[tex]b = 90\%[/tex]

An exponential function is represented as:

[tex]f(x) = ab^x[/tex]

Substitute values for (a) and (b)

[tex]f(x) = 100 \times (90\%)^x[/tex]

Express percentage as decimal

[tex]f(x) = 100 \times (0.9)^x[/tex]

After 5 hours, the value of x is 5

i.e. x = 5

So, we have:

[tex]f(x) = 100 \times (0.9)^5[/tex]

Evaluate the exponent

[tex]f(x) = 100 \times 0.59049[/tex]

Multiply

[tex]f(x) = 59.049[/tex]

Approximate

[tex]f(x) = 59[/tex]

Hence, there were 59 bacteria after 5 hours

Read more about exponential population function at:

https://brainly.com/question/20115298