Question

Tia and Shaan each opened a savings account on the same day. The balance in the savings account t years after it was opened is given by these equations. Tia: Balance =440+45t Shaan: Balance =300(1.20)^t After how many years will Shaun's savings account have a greater balance than Tia's? Clearly show your strategy for solving.

Answer 1

After 4 years, Shaun's savings account will have a greater balance than Tia's.

Step-by-step explanation:

To find out after how many years Shaun's savings account will have a greater balance than Tia's, we need to set up an equation and solve for t.

Tia's balance equation is: Balance = 440 + 45t

Shaan's balance equation is: Balance = 300 * (1.20)^t

Let's set the two equations equal to each other and solve for t:

440 + 45t = 300 * (1.20)^t

To solve this equation, we can use numerical methods or graphing to find the intersection point. However, for simplicity, let's use estimation and substitute values for t until we find the closest solution.

After substituting values, we find that at t = 4, Shaun's balance will exceed Tia's balance. Therefore, after 4 years, Shaun's savings account will have a greater balance than Tia's.