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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**(a) Determine the number of trips until the account is empty**

Ivanna’s account balance after $$ t $$ trips is given by 
$$
A(t)=224-14t.
$$
To find when her account is empty, set $$ A(t) $$ equal to 0:
$$
224-14t=0.
$$
Now, solve for $$ t $$:
$$
14t=224 \quad \Longrightarrow \quad t=\frac{224}{14}=16.
$$
Thus, Ivanna can take **$$ 16 $$ trips** until her account is empty.

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**(b) Calculate the amount remaining after 9 trips**

Substitute $$ t=9 $$ into the function:
$$
A(9)=224-14 \times 9.
$$
First, compute the cost for 9 trips:
$$
14 \times 9=126.
$$
Then, subtract this from the initial amount:
$$
A(9)=224-126=98.
$$
Thus, after 9 trips, Ivanna has **$$ \$98 $$** left in her account.
**(a) Ivanna can take 16 trips until her account is empty.** **(b) After 9 trips, she has \$98 left in her account.**

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