Understanding Exponential Growth and Decay: A Guide to the Formula A(t)=P(1 +/- r)^t

A(t)=P(1 +/- r)^t

general exponential growth/decay formula

The formula A(t)=P(1 +/- r)^t is an exponential growth or decay formula, where A(t) represents the amount at time t, P represents the initial amount, r represents the rate of growth or decay, and t represents the time elapsed.

If r is a positive number, this represents exponential growth and if r is a negative number, it represents exponential decay.

To use this formula to solve a problem, we can follow these steps:

1. Identify the values of P, r, and t.
2. Determine whether the problem involves growth or decay and adjust the sign of r accordingly.
3. Plug in the values into the formula and simplify.

Example:

Suppose you deposit $1000 in a savings account that earns an annual interest rate of 5%. What will be the value of the account after three years, assuming the interest is compounded annually?

Solution:

1. P = 1000 (initial amount)
r = 0.05 (annual interest rate)
t = 3 (time in years)

2. The problem involves growth, so we don’t need to adjust the sign of r.

3. Plug in the values into the formula:

A(t)=P(1+r)^t
A(3) = 1000(1+0.05)^3
A(3) = 1000(1.157625)
A(3) = $1157.63

Therefore, the value of the account after three years would be $1157.63.

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