Question

PLEASE HELP ALGABRA 1

Tyler is going on a hiking trip. At the end of the
first day he has 7,250 feet left to climb. He plans
to climb 400 feet each day.

Write an explicit formula to model the situation.

At the end of which day does Tyler have 1750
feet left to climb?

Answer 1

(1) F(n) = 8050 -400n

(2) 16 days

Explanation:

Tylor first day he has left 7,250feet left to climb, this means that he has already climbed his 400ft on his first day

This will produce an arithmetic series for the distances left to climb as each day passes

initial climb = 7,250+400 = 7,650

Arithmetic Series

7650 , 7250 , 6850 , 6450 ......

a = 7650 , d = -400

(1) Explicit formula

F(n) = a + (n-1)d

= 7650 + (n-1)(-400)

= 7650 +400 -400n

F(n) = 8050 -400n

(2) 8050 -400n = 1750

6300 = 400n

n = 6300 /400 = 15.75 = 16 days( approximately)

So after 16days (approximately) Taylor will have 1750ft left to climb.