Exercise 10 Page 277

Practice makes perfect

We know that a bacterial population is represented by an exponential function.

y= a* b^xIn this function a is the y-intercept, or the initial value. The points (0, 100) and (1,200) lie on the function. Then, a= 100. y= 100* b^x To find the value of b we will substitute the point (1,200).

y=100* b^x

SubstituteII

x= 1, y= 200

200=100* b^1

▼

Solve for b

DivEqn

.LHS /100.=.RHS /100.

2=b^1

BaseOne

1^a=1

2=b

RearrangeEqn

Rearrange equation

b=2

We can now write the function that represents the bacterial population. y=100* b^x ⇒ y=100* 2^x

To find the population after 6 days, we will substitute 6 for x into the function.

y=100* 2^x

Substitute

x= 6

y=100* 2^6

CalcPow

Calculate power

y=100 * 64

Multiply

y=6400

The population will be 6400 after 6 days.

The bacterial population in the previous example grows faster than this bacterial population.

y= 100* 2^x & (I) y= 3* 4^x & (II) Although the initial value of Function (I) is greater than that of Function (II), the constant multiplier of Function (II) is greater than the other function's multiplier. Each time the value of Function (II) is multiplied by 4 and, therefore, Function (II) grows faster.

Subchapter links

Communicate Your Answer p.273

Monitoring Progress p.274-277

Exercises p.278-280

Exercise 10 Page 277

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