Final answer:
The equation Susanna can use to calculate how many years it will take for the value of the account to reach $600 is 1.5 = (1.03)^t. By taking logarithms of both sides and solving for t, we find that it will take approximately 9.41 years.
Step-by-step explanation:
To find the equation to calculate how many years it will take for the value of the account to reach $600, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal (or deposit), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, we know that Susanna deposits $400, the interest rate is 3% (or 0.03), interest is compounded annually (n = 1), and the final amount A is $600. So the equation would be:
600 = 400(1 + 0.03/1)^(1t)
Simplifying this equation:
1.5 = (1.03)^t
Next, we can solve this equation for t by taking logarithms, specifically the natural logarithm (ln), of both sides:
ln(1.5) = ln(1.03)^t
t ln(1.03) = ln(1.5)
t = ln(1.5) / ln(1.03)
Using a calculator to evaluate this, t ≈ 9.41 years. Therefore, it will take approximately 9.41 years for the value of the account to reach $600.