In the year 2016, a total of 20 million people took a vacation to DisneyWorld. The number of DisneyWorld visitors has been growing at a rate of approximately 4% per year for the last five years. Write a formula to approximate the number, N, of visitors in millions of t years after 2016.
Exponential Growth Key words: growing at a rate, 4% per year Formula for exponential growth $$ab^t$$ - $$a$$ represents the initial population - $$b$$ represents the growth factor -$$t$$ represents the time; in this came it would be (years) Note: - "Starting at year 2016, a total of 20 million people took a vacation to DisneyWorld" (the statement above represents the initial population of year 2016) - "growing at a rate of approximately 4% per year" (the statement above represents the annual growth rate of people vacationing at DisneyWorld) Note: - "for the last five years" (don't be tricked by that portion because it represents the credibility and accuracy of the growth rate) In order to use the exponential growth formula , $$ab^t$$, we must find the initial population and growth factor. In order to find the initial population, you must look for keywords in the text such as "Year 2016, a total of 20 million people took a vacation to DisneyWorld" which represents a population. Initial Population => $$20$$ $$million$$ In order to find the growth factor we must find the growth rate add with 1.00 Growth Factor = ?????? Growth Factor = Growth Rate + $$1.00$$ => ($$b$$) = ($$r$$ + $$1.00$$) In order to find the growth rate, we must look for keywords in the text such as "growing at a rate of approximately 4% per year" Growth Rate => $$4%$$ or $$0.04$$ Therefore, Growth Factor => $$1.04$$ = $$0.04 + 1.00$$ Now, we plug in the numbers we found back into the formula: $$ y$$ $$=$$ $$20(1.04)^t$$
Every summer, you go to your community's fair. They have come out with a new promotion this year to get more business. Entrance to the fair is $10.00 and the first ten ride tickets you buy cost $2.00 per ticket. The next five ride tickets cost $1.00 per ticket. Every ride ticket thereafter costs 50 cents per ticket. Find a formula(s) for the cost, C(n), of going to the fair and buying, n, tickets, in dollars.
Note: - entrance to fair is $10.00 - first ten ride tickets = $2.00 $$C(n) = 10.00 + 2.00n ; 0 \leq n \leq 10$$ Note: - next five ride tickets = $1.00 $$C(n) = 30.00 + 1.00(n-10) ; 10 < n \leq 15$$ (***The "n-10" are the ride tickets you already paid for, so you must subtract it that amount from the next equation) Note: -ever ride ticket thereafter costs 50 cents per ticket $$C(n) = 35.00 + 0.50(n-15) ; 15 < n$$ (***The "n-15" are the ride tickets you already paid for from the first and second equation, so you must subtract is from the third equation)