Exponential Growth & Decay
A population is modeled by p(t) = 500(1.04)t
What is the initial population?
500
Solve the matrix. Write undefined if it cannot be solved.
[0 2] - [3 2]
[-3 0]
| p - 2 | = 11
Let f(x) = 4x - 7
Find f(3). Identify the input and the output.
f(3)=5
Input is 3, output is 5.
Find the next number in the sequence.
4 , -20 , 100 , -500 , ___________
2,500
A savings account balance is compounded annually. The interest rate is 4% per year and the current balance is $1,198.
Write a function to model this situation.
1,198(1+0.04)t or 1,198(1.04)t
Solve the matrix. Write undefined if it cannot be solved.
5[3 4]
[15 20]
| 9 - x | = 16
{7 , -25 }
Let g(x) = -2x + 9
Find g(-5). Identify in input and the output.
g(-5) = 19
Input is -5, output is 19.
Identify whether the statement represents a discrete or continuous relationship.
For every ton of paper that is recycled, 17 trees are saved.
discrete
A country pledges to reduce its annual CO2 emissions by 5% per year. The initial emissions were 4,490 Mt.
Write a function to model this situation.
4,490(1 - 0.05)t or 4,490(0.95)t
Timmy evaluates valid matrix operations. Which operation is valid?
a. adding matrices of different sizes
b. subtracting matrices of the same size
c. adding a scalar to a matrix
b. subtracting matrices of the same size
| n + 4 | < 14
-18 < n < 10
If f(x)=3x+4, and f(x) = 19, solve for x.
x = 5 because 19 = 3(5) + 4
Solve for x. Show your work.
12x = 25.80
x = 2.15
A bacteria population starts at 50 and triples every hour. Write a function that models the population after t hours.
50(3)t
A data analyst works with matrices representing different data sets. Which two statements about matrix operations are true?
a. matrices must be the same size to add or subtract
b. scalars multiply each entry in a matrix
c. matrices of different sizes can always be added
d. subtraction changes the size of a matrix
A and B
Matrices must be the SAME size to add and subtract. Scalars multiply each entry in the matrix.
| a + 5 | < 1
-6 < a < -4
If h(x) = 2x and h(x) = 32, find x.
x = 5 because 25= 32
Simplify the equation to find the slope.
y = 3( x - 2 ) + 5
y = 3x - 1, the slope is 3
Select 2 answers.
A car starts at $25,000 and loses 20% of its value each year. Which functions correctly model the value after t years?
a. 25,000(0.20)t
b. 25,000(0.80)t
c. 25,000(1 - 0.20)t
d. 25,000(1.20)t
B and C
Multi-select (2 answers)
A retail company tracks sales across two days using matrices. Which situations can be solved using only matrix addition or subtraction?
a. combining total sales from two different days
b. applying a 7% tax increase to all prices
c. finding the difference in attendance between two years
d. doubling all values in the data set
A and C
| b + 8 | + 10 = 22
{ 4 , -20 }
Write a linear function for the scenario. A car service charges $10 per hour.
Indicate if the relationship is linear or exponential and if the context is best modeled as a discrete or continuous.
For every hour that passes, the amount of area infected by the bacteria doubles.
continuous, exponential