IM Algebra Unit 5 Review

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(b^x), where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What does it mean for a function to increase by a certain percentage?

Back

It means that for every unit increase in 'x', the function's value increases by that percentage of its current value.

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What is the growth factor in an exponential function?

Back

The growth factor is the base 'b' in the function f(x) = a(b^x), which indicates how much the function multiplies for each unit increase in 'x'.

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How do you calculate the decay of a population over time?

Back

Use the formula P(t) = P0(1 - r)^t, where P0 is the initial population, r is the decay rate, and t is the time in years.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is P(t) = P0(1 + r)^t, where P0 is the initial amount, r is the growth rate, and t is the time.

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What does a decay rate of 10% mean in terms of population?

Back

A decay rate of 10% means that each year, the population decreases to 90% of its value from the previous year.

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How do you determine if a function is increasing or decreasing?

Back

A function is increasing if its derivative is positive, and decreasing if its derivative is negative.

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 multiplier in a table of values?

Back

The multiplier is the constant factor by which the output values increase or decrease as the input values change.

Front

How do you find the value of an exponential function at a specific point?

Back

Substitute the value of 'x' into the function f(x) = a(b^x) and calculate the result.