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.

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.

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.

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.

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.

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.

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.

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.

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.