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Chapter 9: Q49. (page 595)

The population of bacteria in a petri dish increases according to the modelp=550(2.7)0.008t, wheretis the number of hours and t=0corresponds to1:00P.M. Use this model to estimate the number of bacteria in the dish at 5:00P.M.

Short Answer

Expert verified

The numbers of bacteria on the dish at 5:00PMare 567.76.

Step by step solution

01

Step 1. State the concept of Exponential function.

An exponential function is a function of the formy=abx where a鈮�0, b>0, and b鈮�1.

02

Step 2. Estimate the value of t. 

The equation p=550脳(2.7)0.008t, where tis the number of hours since 1:00PM

twill be the time between 1:00P.M to 5:00P.M.

Therefore, t=5.00PM鈥�1.00PM=4hours.

03

Step 3. Simplify for p.

Substitute 4 for tinto the equation p=550脳(2.7)0.008tand simplify for p.

p=550脳(2.7)0.008t=550脳(2.7)0.008鈥夆赌�脳鈥�4=567.76

The numbers of bacteria on the dish at 5:00PM are 567.76.

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