Exponential Rate of Change

What is the average rate of change of the graph over the interval [-2,0]?

• -3/2

• 2/3

• 3/2

• -2/3

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Which of the following represents an exponential decay function?

Tags

CCSS.HSF-LE.A.1A

On the first day of a measles outbreak at a school, 5 students were identified to have the measles. Each day for the following two weeks, the number of new cases doubled from those identified with the disease the day prior. 

How many students are identified to have measles in all at the end of the 6^th day of the outbreak?

• 286

• 315

• 345

• 378

Tags

CCSS.HSF.BF.A.2

James' 70 in. giant peach doubles in size every week. Write an expression that would represent how big the peach is after 5 weeks.

• 70(2)³⁵

• 70(2)⁵

• 2(70)⁵

• 5(70)²

Tags

CCSS.HSF.BF.A.2

What is the Average rate of change formula? (Rate of change of Exponential Functions)

• (f(a) + f(b)) / (b + a)

• (f(b) - f(a)) * (b + a)

• (f(a) * f(b)) / (b - a)

• (f(b) - f(a)) / (b - a)

Answer explanation

The average rate of change of a function between two points a and b is calculated using the formula (f(b) - f(a)) / (b - a). This measures how much the function value changes per unit change in x, making it the correct choice.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Find the average rate of change over the given interval. 

• 4

• 7

• 7/3

• 3/7

Answer explanation

To find the average rate of change, use the formula (f(b) - f(a)) / (b - a). After calculating for the given interval, the result simplifies to 7/3, making it the correct choice.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

James bought a car worth $22,000 that loses 10% of its value every year. The value of the car after x years can be modeled by the function f(x) = 22,000(.9)^x.

What is the average rate of change between 0 and 4 years?

• $-1,100/year

• $-1521.12/year

• $-1,776/year

• $-1,891.45/year

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

What is the average rate of change between when x = -1 and x = 0?

• -2

• 2

• 1/2

• -1/2

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

What is the average rate of change over the interval [0,3]?

• 21

• -21

• 1/21

• -1/21

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Iris founded a new town, Iristown. The population of Iristown after x years can be modeled by the function p(x) = 1500(1.1)^x. On average, how fast is the population increasing between years 0 and 10?

• 212.12 people/year

• 251.11 people/year

• 239.06 people/year

• 391.29 people/year

Tags

CCSS.HSF-IF.C.8B