Common 10 #4 Retake

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is given by: \(y = a(1 + r)^t\), where \(a\) is the initial amount, \(r\) is the growth rate, and \(t\) is time.

Front

Define compound interest.

Back

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Front

What does the term 'exponential function' refer to?

Back

An exponential function is a mathematical function of the form \(f(x) = a b^x\), where \(a\) is a constant, \(b\) is the base of the exponential, and \(x\) is the exponent.

Front

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

Back

The base in an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents growth; if it is between 0 and 1, it represents decay.

Front

How do you calculate the total amount in a savings account with compound interest?

Back

The total amount \(A\) in a savings account with compound interest can be calculated using the formula: \(A = P(1 + r/n)^{nt}\), where \(P\) is the principal, \(r\) is the annual interest rate, \(n\) is the number of times interest is compounded per year, and \(t\) is the number of years.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is given by: \(y = a(1 - r)^t\), where \(a\) is the initial amount, \(r\) is the decay rate, and \(t\) is time.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage over equal intervals.

Front

What does the term 'initial value' mean in the context of exponential functions?

Back

The initial value in an exponential function is the value of the function when \(x = 0\), often represented as \(a\) in the function \(y = ab^x\).

Front

How can you identify an exponential function from a table of values?

Back

An exponential function can be identified from a table of values if the ratio of consecutive outputs is constant.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is \(y = a(1 + r)^t\) or \(y = ab^x\) with \(b > 1\).