GMAS: Exponential growth/decay

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is y = a(1 + r)^t, where 'a' is the initial value, 'r' is the growth rate, and 't' is time.

Front

What does the base of an exponential function represent in the context of growth?

Back

The base of an exponential function represents the growth factor, which indicates how much the quantity increases for each time period.

Front

In the function v(t) = 30,000(1.125)^t, what does the value 30,000 represent?

Back

The value 30,000 represents the initial value of the investment.

Front

How do you determine the growth rate from an exponential function?

Back

The growth rate can be determined by subtracting 1 from the base of the exponential function. For example, in y = a(1 + r)^t, the growth rate r is found as r = base - 1.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases over time, while exponential decay occurs when a quantity decreases over time.

Front

In the equation y = 48000(1.024)^{10}, what does the exponent represent?

Back

The exponent represents the number of time periods (in this case, years) over which the growth is being calculated.

Front

What does the initial value represent in an exponential function?

Back

The initial value represents the starting amount or quantity before any growth or decay has occurred.

Front

In the function f(x) = 100(2)^t, what does the number 2 represent?

Back

The number 2 represents the growth factor, indicating that the population doubles for each time period.

Front

What is the significance of the growth factor in an exponential function?

Back

The growth factor indicates how much the quantity will multiply by for each unit increase in time.

Front

In the function s(t) = 273(1.073)^t, what does the value 0.073 represent?

Back

The value 0.073 represents the growth rate of the population of gray squirrels.