SMI ES Q3 Exponentials (Post)

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 does the variable 'a' represent in the exponential function f(x) = a(1 + r)^x?

Back

'a' represents the initial value or starting amount before growth.

Front

How do you convert a percentage to a decimal for use in exponential functions?

Back

Divide the percentage by 100. For example, 3% becomes 0.03.

Front

What is the exponential function for a savings account with an initial deposit of $1500 and an annual interest rate of 1.5%?

Back

f(x) = 1500(1 + 0.015)^x.

Front

If a savings account has an initial amount of $400 and grows at a rate of 3% per year, what is the exponential function?

Back

f(x) = 400(1 + 0.03)^x.

Front

What is the initial value in the function y = 6.87(4)^x?

Back

The initial value is 6.87.

Front

How do you express a 35% increase in an exponential function?

Back

You express it as f(x) = initial amount(1 + 0.35)^x.

Front

What is the exponential function for an initial amount of $15 with a 35% increase each year?

Back

y = 15(1.35)^x.

Front

What type of growth is represented by the function f(x) = a(1 + r)^x?

Back

Exponential growth.

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.