Assignment #33

Front

What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.

Front

What is the formula for exponential growth?

Back

The formula is f(t) = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What does a growth factor of 1.05 indicate?

Back

A growth factor of 1.05 indicates a 5% increase in value.

Front

How do you determine the growth rate from a function?

Back

The growth rate can be found by identifying the base of the exponential function in the form f(t) = a(1 + r)^t.

Front

What is the initial amount in an exponential function?

Back

The initial amount is the value of the function when time (t) is zero, represented by 'a' in the formula.

Front

If a car's value increases by 8% per year, what is the growth factor?

Back

The growth factor is 1.08.

Front

How do you write an exponential growth function for a quantity that starts at 6 and grows at 14% per week?

Back

The function is y = 6(1.14)^x.

Front

What is the difference between growth rate and growth factor?

Back

The growth rate is the percentage increase, while the growth factor is the multiplier used in the exponential function.

Front

What does it mean if a function has a base less than 1?

Back

A base less than 1 indicates exponential decay, meaning the value decreases over time.

Front

How can you identify exponential growth from a table of values?

Back

Exponential growth can be identified if the ratio of consecutive values remains constant.