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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 18 Page 265

Practice makes perfect

a We want to write an exponential function that represents the given problem.

y= a* b^x Here, a is the y-intercept and b is the constant multiplier. In order to write our function we have to find these values using the given information. We are told that at the beginning, when time is 0 hours, there are 5000 bacteria. As such, the y-intercept and the value of a is 5000. y= 5000* b^x After 8 hours, there are 28 000 bacteria in the sample. We can substitute x= 8 and y= 28 000 into the partial equation to find the value of b.

y=5000* b^x

x= 8, y= 28 000

28 000=5000* b^8

▼

Solve for b

Rearrange equation

5000* b^8=28 000

.LHS /5000.=.RHS /5000.

b^8=5.6

sqrt(LHS)=sqrt(RHS)

b=sqrt(5.6)

Use a calculator

b=1.240290...

Round to 2 decimal place(s)

b≈ 1.24

Finally, we can write the equation that models the bacteria population in the sample. y≈ 5000* 1.24^x ⇔ y≈ 5000(1.24)^x

b To find the expected number of bacteria after 32 hours we will use the equation found in Part A.

y≈ 5000(1.24)^x To find how many bacteria can be in the sample after 32 hours, we have to substitute x= 32 into our equation. Let's do it!

y≈ 5000(1.24)^x

x= 32

y≈ 5000(1.24)^(32)

Use a calculator

y≈ 4 880 495.64445...

Round to nearest integer

y≈ 4 880 496

After 32 hours, about 4 880 496 bacteria can be expected in the sample.

Subchapter links

1 Graphing Exponential Functions p.265

2 Solving Exponential Equations and Inequalities p.265

3 Simplifying Radical Expressions p.265

4 Operations with Radical Expressions p.266

5 Radical Equations p.266