Final answer:
An equation to represent the amount of money in the account is A = 750(1 + 0.015)^t.
In this case, it takes approximately 7.65 years for the account balance to reach $1346.89.
Step-by-step explanation:
To represent the amount of money in the savings account as a function of time in years, we can use the formula for compound interest: A = P(1 + r/n)^(nt). ( Where A is the amount in the account after time t, P is the initial deposit, r is the annual interest rate in decimal form, n is the number of times the interest is compounded per year, and t is the time in years).
In this case, the formula becomes: A = 750(1 + 0.015)^t.
To find the amount of time it takes for the account balance to reach $1346.89, we can set up the equation:
1346.89 = 750(1 + 0.015)^t.
Let's solve for t:
- Divide both sides of the equation by 750: (1 + 0.015)^t = 1.79586
- Take the logarithm (base 1+0.015) of both sides: t = log(1.79586) / log(1 + 0.015)
- Calculating the logarithms, we find that t ≈ 7.65
So, it takes approximately 7.65 years for the account balance to reach $1346.89.