Change in Linear and Exponential Functions

Given the function values x = 2, 6, 10 and f(x) = 12, 9, 6, what type of function is represented?

• Linear function

• Exponential function

• Quadratic function

• Logarithmic function

What type of function is described if for each input change of 4, the function changes at a constant rate of -3?

• Linear

• Exponential

• Quadratic

• None of the above

The population of Cary, NC in the year 2000 was 97,400 people. The population steadily grew by 2.5% each year. Which function relates to the situation? Let Population (P) be a function of time (t)

• P(t)=97400+2.5t

• P(t)=97400(2.5)^t

• P(t)=97400(1.25)^t

• P(t)=97400(1.025)^t

The amount of fertilizer in a landscaping company’s warehouse decreases at a rate of 3% per week. The amount of fertilizer in the warehouse was originally 78,000 cubic yards. Which function models the amount of fertilizer in cubic yards left after w weeks?

Function A is linear and starts with $1000 and increases by $100 each day y=100x+1000 Function B is exponential and begins with $20 but doubles each day y = 20(2)^x On which interval (domain) does Function B exceed Function A?

• (0,1635.34)

• (0,6.353)

Which statement below describes the comparison of the linear function f(x) and the exponential function g(x)?

• The value of g(x) is always greater than the value of f(x).

• The value of g(x) is never greater than the value of f(x).

• The value of g(x) will eventually exceed the value of f(x).

• There is not enough information to compare the value of f(x) to the value of g(x).

Which statement below describes the comparison of rate of change between the linear function f(x) and the exponential function g(x).

• g(x) rate of change is ALWAYS greater than f(x) rate of change.

• g(x) is NEVER greater than f(x) rate of change.

• g(x) will eventually exceed the rate of change of f(x).

• There is not enough information to compare the rate of change of f(x) to g(x).

Tags

TEKS.MATH.8.5C

Which statements below is TRUE regarding the two functions?

• Both functions are linear

• Both functions are increasing

• Both functions have a y-intercept of 1

• Both functions are exponential growth

• Both functions are exponential decay

A lottery winner must choose between g(x) and h(x) for the distribution of winnings. Each month the distribution increases as shown in the tables. If the payout will last two years, which plan should the winner choose and why?

• The winner should choose g(x) because the table starts with thousands.

• The winner should choose h(x) because it will eventually yield more money.

• g(x) will eventually yield more money than h(x).

There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month. At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January?