# Linear, Quadratic and Exponential Models Practice

## CCSS Algebra Practice

This quiz illustrates the range of difficulty expected by the following Common Core State (CCS) standards:

 Question Common Core Standard # 1 F.LE.1 2 F.LE.1b 3 F.LE.1 4 F.LE.1c 5 F.LE.1c 6 F.LE.2 7 F.LE.3 8 F.LE.4 9 F.LE.5 10 F.LE.5  indicates a modeling standard.

All questions of this quiz illustrate the difficulty of the high school F.LE standards required for all students, including the college and career ready students.

Question 1: Given the exponential functions f(x) = a·2x and g(x) = b·4x, find the values of a and b if both functions intersect in point A of coordinates (1, 2).

Question 2: Which of the functions, f1(x), f2(x) and f3(x) from the table below are quadratic or exponential?

 x f1(x) f2(x) f3(x) 1 5 64 -1 2 7 32 -4 3 9 16 -9 4 11 8 -16 5 13 4 -25 6 15 2 -36

Question 3: A bank account was opened with \$1,000 and a fixed interest of 5%, compounded yearly. After five years, the interest rate was lowered to 3%, also compounded yearly. What is the balance of the account nine years after the account was opened?

Questions 4 and 5: A new species of frogs is released into a pond. The growth of the population of this new species is modeled by P(t) = a·bt , where t is the time in months following the introduction and a and b are positive unknown numbers. After 2 months, the number of frogs is 45 and 3 months after the release, the number of frogs is 135.

The number of frogs released into the pond is:

The value of the exponential base b is:

Question 6: One thousand dollars is invested in a high yield account that pays an interest rate of 7% compounded annually. The first time the sum in the account is more than triple the sum invested is after years.

Question 7: The table below shows values of functions f(x) = 2x and g(x) = x(x + 100) for x ≥ 1:

 x f(x) g(x) 1 2 101 2 4 204 3 8 309 4 16 416 5 32 525

What is the smallest positive non-zero integer x for which f(x) > g(x)?

Question 8: What is the value of x for which f(x) = 10?

Questions 9 and 10: The ticket prices advertised by an airline agency are given in the table below:

 Distance D (miles) Fare F (\$) 510 371 850 405 1530 473

Assuming a linear relation between the distances traveled and fares, if F = a·D + b, then:

 a = 0.08 b = 250 a = 0.1 b = 280 a = 0.15 b = 290 a = 0.2 b = 300 a = 0.25 b = 320

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