Exponential Functions Review

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b^x), where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It represents growth or decay processes.

Front

What does it mean for a population to decrease by a certain percentage each year?

Back

It means that each year, the population is reduced by that percentage of its current size. For example, a 30% decrease means that 70% of the population remains.

Front

Write the equation for a population of 5000 cells decreasing by 30% each year.

Back

y = 5000(0.7)^x

Front

What is the y-intercept of an exponential function?

Back

The y-intercept is the value of 'y' when 'x' is 0. For the function y = a(b^x), the y-intercept is 'a'.

Front

If a population of deer decreases by 1.5% per year, what is the decay factor?

Back

The decay factor is 1 - 0.015 = 0.985.

Front

How do you find the number of deer after 20 years if the initial population is 1500 and decreases by 1.5% per year?

Back

Use the formula y = 1500(0.985)^20.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, denoted as x ∈ ℝ.

Front

What is the range of an exponential function?

Back

The range of an exponential function is all positive real numbers, denoted as y > 0.

Front

What does it mean for a function to have a y-intercept of 1?

Back

It means that when x = 0, the value of y is 1.

Front

If a function has a range of y > -4, what does this indicate about its values?

Back

It indicates that the function's output values are greater than -4, meaning it never reaches or goes below -4.