Math question - please help, i have a math exam in a few days and can't remember how to do it?

Question

this is from a practice exam, but i don't have the answers, so some assistance would be greatly appreciated

k here we go..

The altitude of a plane can be modelled by an exponential equation until it reaches an altitude of 8000 metres.

the altitude, A, (metres) of the plane is given by the equation

A= 5x 1.4^0.457t (to the power of 0.457t)

where t is the time in seconds from take-off.

How long does it take the plane to reach an altitude of 800 metres?

(by the way, the x above is supposed to mean multiplied by)

If you generally use yards, or whatever rather than metres, please humour me and use metres in this equation.

Thank you very much!

Answer 1

Straightforward solution, using logarithms.

5 * 1.4^0.457t = 800

1.4^0.457t = 160

Take logarithm of both sides

log(1.4^0.457t) = log(160)

0.457t * log(1.4) = log(160)

t = log(160) / log(1.4) / 0.457 = 33.005 sec (approx)

Check: 1.4^(0.457*33) * 5 = 799.33 (pretty close)

Answer 2

the equation means that u gotta divide the decimal to the third power so the plane would reach the altitude in 4.57x 15 and then divide it by the unit of time  

Answer 3

A= 5*1.4^(0.457t)

800 = 5*1.4^(0.457t)

160 = 1.4^(0.457t)

log base 1.4 both sides

log(1.4) (160) = 0.457t

t = (1/0.457) log(1.4) (160)

t = 2.188 * 15.1 = 33.0 sec

but I suspect you meant 8000 m

8000 = 5*1.4^(0.457t)

1600 = 1.4^(0.457t)

log base 1.4 both sides

log(1.4) (1600) = 0.457t

t = (1/0.457) log(1.4) (1600)

t = 2.188 * 21.9 = 48.0 sec

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