Question

Emma also wonders how long it will take her balance of $300 to reach $450, assuming she doesn’t make any payments toward it. write the equation to represent the situation, and solve it using the inverse relationship between exponential and logarithmic expressions.

Answer 1

We can use the formula A = P(1 + r)^t where A is the final amount, P is the original amount, r is the interest rate and t is the number of time periods.

In this case, A = $450, P = $300, and r is the interest rate.

450 = 300(1 + r)^t

To solve for t, we can use the inverse relationship between exponential and logarithmic expressions

t = log(A/P) / log(1+r)

Here, A/P = 450/300 = 1.5, log(1.5) is 0.176

The interest rate is not specified, so the exact amount of time is not known. But the equation is log(1.5) / log(1+r) = t.

Explanation: