Final answer:
To find out how long it will take for Ross to have enough money to buy a new bicycle, we need to use the formula for compound interest. By plugging in the relevant values and solving the equation, we find that Ross will need approximately 0.4055 years, or about 4.86 months, to have enough money to buy the new bicycle.
Step-by-step explanation:
In order to find out how long it will take for Ross to have enough money to buy a new bicycle, we need to use the formula for compound interest: A = P × e^(rt), where A is the final amount, P is the principal amount (initial deposit), e is the base of natural logarithms (approximately 2.71828), r is the interest rate, and t is the time in years.
In this case, Ross deposited $300.00, the interest rate is 10%, and the final amount needed is $450.00. Plugging these values into the formula, we get:
450 = 300 × e^(0.10t)
Dividing both sides of the equation by 300 and taking the natural logarithm of both sides, we can solve for t:
ln(450/300) = 0.1t
t = ln(1.5) / 0.1
t ≈ 0.4055 years
Therefore, Ross will need approximately 0.4055 years, or about 4.86 months, to have enough money to buy the new bicycle.