Question

the average annual cost of attending a public, in - state, four - year college was $24,870 in 2018 for one academic year and $27,150 in 2023. what is the average rate of change in the cost between 2018 and 2023?

○ $326

○ $2,280

○ $4,152

○ $456

Explanation:

Step1: Find the change in cost

The cost in 2018 is $24,870 and in 2023 is $27,150. The change in cost is $27,150 - $24,870 = $2,280.

Step2: Find the number of years

The number of years between 2018 and 2023 is 2023 - 2018 = 5 years.

Step3: Calculate the average rate of change

The average rate of change is the change in cost divided by the number of years, so $\frac{2280}{5} = 456$. Wait, no, wait, wait, no, wait, the change in cost is 27150 - 24870 = 2280? Wait, 27150 - 24870: 27150 - 24870 = 2280? Wait, 24870 + 2280 = 27150? Let's check: 24870 + 2000 = 26870, 26870 + 280 = 27150. Yes. Then the number of years is 2023 - 2018 = 5. So average rate of change is 2280 / 5 = 456? Wait, no, wait, 2280 divided by 5: 5*400=2000, 2280-2000=280, 280/5=56, so 400+56=456. Wait, but let's recalculate the change in cost: 27150 - 24870. Let's do 27150 - 24870: 27150 - 24000 = 3150, 3150 - 870 = 2280. Correct. Then 2280 / 5 = 456. Wait, but the options have $456 as an option. Wait, but let me check again. Wait, maybe I made a mistake. Wait, 27150 - 24870 = 2280. 2280 divided by 5: 5*456 = 2280. Yes. So the average rate of change is $456 per year. Wait, but wait, the options: the first option is $326, second $2280, third $4152, fourth $456. So the correct answer is $456? Wait, no, wait, wait, no, wait, 27150 - 24870 is 2280? Wait, 24870 + 2280 = 27150? Let's check: 24870 + 2000 = 26870, 26870 + 280 = 27150. Yes. Then 2280 divided by 5 is 456. So the average rate of change is $456 per year. So the correct option is the one with $456. Wait, but let me check again. Wait, maybe I messed up the years. 2023 - 2018 is 5 years. Correct. So 2280 / 5 = 456. So the average rate of change is $456. So the answer is $456.

Answer:

\$456 (the option with \$456, which is the fourth option if we count the options as: 1. \$326, 2. \$2,280, 3. \$4,152, 4. \$456)