SMI ES Q3 Exponentials (Pre)

Front

What is the formula for exponential growth?

Back

f(x) = a(1 + r)^x, where 'a' is the initial amount and 'r' is the growth rate.

Front

What is the formula for exponential decay?

Back

f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

Front

What does the initial value represent in an exponential function?

Back

The initial value is the starting amount before any growth or decay occurs.

Front

How do you identify the growth rate in an exponential function?

Back

The growth rate is found in the expression (1 + r) in the function f(x) = a(1 + r)^x.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

If a function is represented as f(x) = 3(2)^x, what is the initial value?

Back

The initial value is 3.

Front

What does it mean if a function is classified as exponential decay?

Back

It means that the value of the function decreases over time, approaching zero but never reaching it.

Front

How can you tell if a graph represents exponential growth or decay?

Back

Exponential growth curves upward, while exponential decay curves downward.

Front

What is the formula to calculate the amount after 't' years with continuous compounding?

Back

A = Pe^(rt), where P is the principal, r is the rate, and t is time.