Additional Activity

Front

What is the y-intercept of the function y = 5(3)^x?

Back

The y-intercept is (0, 5).

Front

What is the decay factor for a value decreasing at a rate of 8% per year?

Back

The decay factor is 0.92.

Front

How can you determine if a function represents growth or decay?

Back

If the base of the exponential function is greater than 1, it represents growth; if it is between 0 and 1, it represents decay.

Front

What does exponential decay mean?

Back

Exponential decay refers to a decrease in quantity at a rate proportional to its current value.

Front

What is the general form of an exponential function?

Back

The general form is y = a(b)^x, where 'a' is the initial value and 'b' is the growth/decay factor.

Front

If a car's value is $15,000 and decreases by 8% annually, what will its value be after one year?

Back

The value after one year will be $15,000 * 0.92 = $13,800.

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.

Front

What is the formula to calculate the decay factor?

Back

The decay factor can be calculated as 1 - (decay rate). For an 8% decay rate, the decay factor is 1 - 0.08 = 0.92.

Front

What does the term 'exponential growth' refer to?

Back

Exponential growth refers to an increase in quantity at a rate proportional to its current value.

Front

How do you identify the growth or decay in a graph?

Back

If the graph rises as it moves from left to right, it represents growth; if it falls, it represents decay.