Question

When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the equation representing the number of people, y, at the fair x hours after the gates open.

Answer 1

y=68(1.5)^(x-1)

Explanation:

Answer 2

The function is:

`y = 68 (1.5) ^ x`

Explanation:

Note that the number of people increases by a factor of 1.5 per hour, and the initial number of people is 68.

So:

After an hour the number of people is:

`y = 68 (1.5)`

After two hours the number of people is:

`y = 68 (1.5) (1.5) = 68 (1.5) ^ 2`

After x hours the number of people is:

`y = 68 (1.5) ^ x`

Therefore, the exponential growth function that models the number of people y at the fair after x hours is:

`y = 68 (1.5) ^ x`