homen mula Ivanna spends \( \$ 14 \) each time she travels the toll roads. She started the month with \( \$ 224 \) in her toll road account. The amount, \( \mathbf{A} \) (in dollars), that she has left in the account after \( t \) trips on the toll roads is given by the following function. \[ A(t)=224-14 t \] Answer the following questions. (a) How many trips on the toll roads can Ivanna take until her account is empty? \( \square \) trips (b) How much money does she have left in the account after 9 trips on the toll roads? \[ 50 \]
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To find out how many trips Ivanna can take until her account is empty, we need to set \( A(t) \) to zero and solve for \( t \): \[ 0 = 224 - 14t \] Rearranging gives: \[ 14t = 224 \quad \Rightarrow \quad t = \frac{224}{14} = 16 \] So, Ivanna can take \( \boxed{16} \) trips before her account is empty. For part (b), we simply plug in \( t = 9 \) into the function \( A(t) \): \[ A(9) = 224 - 14 \times 9 = 224 - 126 = 98 \] Therefore, after 9 trips, she has \( \boxed{98} \) dollars left in her account.