Unit 7 Review

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.

Front

What does the equation f(x) = 125(0.65)^t represent in terms of population decrease?

Back

It represents a situation where the population decreases by 35% each year, starting with 125 chickens.

Tags

CCSS.HSF.LE.B.5

Front

What is the value of f(0) in the function f(x) = b^x?

Back

f(0) = 1, because any non-zero number raised to the power of 0 is 1.

Tags

CCSS.HSF-IF.C.8B

Front

How do you find the nth term of a geometric sequence?

Back

Use the formula a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio in the sequence 3, 6, 12, 24, 48, 96?

Back

The common ratio is 2, as each term is multiplied by 2 to get the next term.

Tags

CCSS.HSF.BF.A.2

Front

How do you calculate compound growth over time?

Back

Use the formula A = P(1 + r)^t, where A is the amount after time t, P is the principal amount, r is the growth rate, and t is the time.

Tags

CCSS.HSF-LE.A.1C

Front

What is the formula for exponential decay?

Back

The formula is f(t) = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Tags

CCSS.HSF-LE.A.1A

Front

If the attendance at a museum is increasing by 3% each month, how do you express this mathematically?

Back

You can express it as A = 250(1 + 0.03)^t, where A is the attendance after t months.

Tags

CCSS.HSF-LE.A.1C

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for the 19th term of the sequence 3, 6, 12, 24, 48, 96?

Back

Using the formula a_n = a_1 * r^(n-1), the 19th term is 3 * 2^(19-1) = 786432.

Tags

CCSS.HSF.BF.A.2