Mathardy

Exponential Functions

100

A sample contains 2 cells, the number of cells doubles every half hour. How much are there after half a day?

16,777,216 Cells.

200

In 1986, Fort Lauderdale had a population of around 15,000 people, the population increased at a rate of 3% annually, Write an equation to explain the current population after X years.

15,000(1.03)^x = y

300

The value of a certain gem after X years is modeled by the expression 65,454(0.82)^x. What is the initial cost, and rate of depreciation?

$65454, 18%.

400

In 2019, the enrollment at Lexington Middle School was 643 students. The equation P(t) = 643(0.8)^t can be used to determine the number of students enrolled t years after 2019. Is the rate of enrollment appreciating or depreciating, and at what rate.

It is depreciating, at a rate of 20%.

500

Given the function F(t) = 650(2.4)^2t

A. 1560^t 

B. 3744^t

C. 650(5.76)^t

D. 650(4.175)^t

B. 3744^t

Polynomials

100

(4x³+7x²+2x)+(5x³+4x²-3x)

9x³+11x²-x

200

Perform the proper operation to make this equation a trinomial.

(x+7)(x-4)

x²+3x-28

300

Make a perfect trinomial out of the squared binomial (-8x+3)².

64x²-48x+9

400

4(2x²+4x-20)-(3x²+2x+13)

5x²+14x-93

500

Find the values of t, b, m, so that (5x+8)(1x-6) = tx²+bx+m.

t = 5

b = -22

m = -48

Absolute Value Functions

100

|7n-12| = 25 Solve for n rounding to the nearest hundreth.

5.29, -1.86

200

-|3x+8|+9=-18 Solve for x rounded to the nearest hundredth place.

9.67, -15.33

300

Find the value v rounded to the nearest hundredth.

7|4v+16|-16 = -5

-3.61, -4.39

400

Thomas has a budget of $500 for a new air conditioner, he finds two air conditioners that are $25 above and $25 below his budget, write an absolute value equation that can be used to find the prices of the air conditioner. And what are the prices of the air conditioners.

0 = |x-500|-25,

475, 525

500

The Ivankovic family buys 213 water bottles at the local Home Depot, the total is $24.25 above or below $426, write an absolute value equation that models the cost x, in dollars, of a single dozen of water bottles rounded to the nearest hundredth.

|17.75x-426|-24.25 = 0

22.63, 25.38

Linear Equations

100

A machine on a production line packages sofas at a steady rate. After 15 minutes, it has packaged 40 sofas, and after 45 minutes it has packaged 100 sofas, write an equation to model y sofas packed after X minutes,

y = 2x+10

200

Write a linear function for a line that passes through the point (7,4) and is perpendicular to y = 3.5x+8

y = -1/3.5+6

300

Louis hikes at a steady rate from a police station to a school 30 miles away. After 5 hours he is 11 miles away, after 10 hours he is 7 miles away. if a graph were to be made if this hike, what would be the slope and what would it represent?

-0.8; how close he gets to the school after 1 hour.

400

16x+5y = 8, what is the slope?

-3.3 or 16/5

500

13x+6.5y = 24, what is the x intercept, y intercept, slope, domain, and range, rounded to the nearest hundredth if needed?

1.85, 3.69, -2, all real, all real.

Laws of Exponents

100

Rewrite the expressions, 5^1/5 and x^1/6y^1/2 in radical form.

5th root of 5¹, 3rd root of (xy)²

200

Simplify (x⁴)(x^1/9)³(x^7/4) = x^?

x^{6 1/12} 

300

? root of 4³ = 4, what must ? be to make the equation true?

3

400

identify the equation that is equal to the square root of 48?

a. 3 * square root of 4

b. 3 * square root of 16

c. 4 * square root of 3

d. 4 * square root of 8

c. 4 * square root of 3

500

Multiply cube root of 216 by cube root of -8.

-12