Question

Noa drove from the Dead Sea up to Jerusalem, and her altitude increased at a constant rate of 740 meters per hour. When she arrived in Jerusalem after 1.5 hours of driving, her altitude was 710 meters above sea level.

Let A(t) denote Noa's altitude relative to sea level A (measured in meters) as a function of time t (measured in hours).

Answer 1

hmm, so

A(t)=740t+a₀
where a₀ is initial height or the height she started at

we want to find her initial height

after 1.5 hours, she was 710 meters above sea levl
alright
A(1.5)=740(1.5)+a₀=710
740(1.5)+a₀=710
1110+a₀=710
minus 1110 both sides
a₀=-400


so she stared at -400 meters below sea level

and the equation would be (or function)
A(t)=740t-400

Answer 2

She stared at -400 meters below sea level and the equation is A(t)=740t-400

Functions and values

Functions are written in terms of variables

From the given question;

Let a₀ is the initial height or the height she started at

Required

Initial height

After 1.5 hours, she was 710 meters above sea level

Substitute the given time into the function

A(1.5)=740(1.5)+a₀=710

740(1.5)+a₀=710

1110+a₀=710

a₀=-400

This shows that she stared at -400 meters below sea level and the equation is A(t)=740t-400

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