Exponential and Linear Relationships in Mathematics

These flashcards cover key concepts related to exponential and linear relationships from the lecture notes, focusing on mathematical relationships, functions, and properties of exponents.

What type of relationship exists between tickets sold and profit in Sam's movie theater?

Discrete

Why is the relationship between hours and square feet of bacteria considered exponential?

Because the bacteria is growing by a factor of 3 every hour.

What is the domain for the function that models the relationship between hours and square feet of bacteria?

x is continuous and time is represented by positive numbers.

What explicit function models the relationship between hours and square feet of bacteria?

f(x) = 4(3)^x

Is the relationship between workers and bricks laid linear or exponential?

Linear, because the number of bricks increases by 90 for every additional worker.

What is the domain for the function modeling the relationship between workers and bricks laid?

{x | x ∈ N}, where N includes 1, 2, 3, 4.

What is the explicit rule for the relationship between workers and bricks laid?

f(x) = 90x

What is the recursive rule for the relationship between workers and bricks laid?

f(x) = 90 + f(x-1); f(1) = 90.

How is the value of 2^5 determined using the properties of exponents?

It means 2 multiplied by itself 5 times.

How is the expression 9x^(4x²) simplified in exponential form?

(9x^(4x²))² = 3x²y.

What is the significance of having only positive exponents in simplified expressions?

It makes the expressions easier to read and understand.

What is the range for an exponential function with an asymptote?

The range is often all positive values greater than the asymptote.

What can be inferred from the statement 7^2 means?

7 multiplied by itself 2 times, resulting in the number 49.

For the function y = 2 + 6, what would you identify as its y-intercept?

y-intercept is 2.