1B Exponential Growth

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 general form of an exponential function?

Back

The general form is f(x) = a(b)^x, where 'a' is the initial amount, 'b' is the base, and 'x' is the exponent.

Front

In the expression 2^3 = 8, what is the base?

Back

The base is 2.

Front

Solve for x: 3x - 6 = 18.

Back

x = 8.

Front

Evaluate the expression f(x) = 2(3)^x for f(5).

Back

f(5) = 486.

Front

What does the 'a' represent in the function f(x) = 300(1.16)^x?

Back

The 'a' represents the initial amount, which is 300.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept is the value of the function when x = 0.

Front

If f(x) = 300(1.16)^x, what is f(0)?

Back

f(0) = 300.

Front

What is the growth factor in the function f(x) = 300(1.16)^x?

Back

The growth factor is 1.16.

Front

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

Back

Substitute the value of x into the function and calculate.