Simple comparison

Algebra Level 2

Let A = 1.0 8 9 A = 1.08^9 and B = 1.0 9 8 B = 1.09^8

Which is true?

A > B A < B Insufficient information to compare the values of A and B A = B

Denton Young by Denton Young , 47, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Chew-Seong Cheong
Dec 13, 2017

Consider A B = 1.0 8 9 1.0 9 8 = 1.08 ( 1.09 − 0.01 ) 8 1.0 9 8 > 1.08 ( 1.0 9 8 − 8 ( 1.0 9 7 ) ( 0.01 ) ) 1.0 9 8 = 1.08 − 0.0864 1.09 > 1 \dfrac AB = \dfrac {1.08^9}{1.09^8} = \dfrac {1.08(1.09-0.01)^8}{1.09^8} > \dfrac {1.08(1.09^8-8(1.09^7)(0.01))}{1.09^8} = 1.08 - \dfrac {0.0864}{1.09}> 1

⟹ A > B \implies \boxed{A>B} .

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Denton Young
Dec 11, 2017

A = ( 1.009667 ) 72 A = (1.009667)^{72}

B = ( 1.009621 ) 72 B = (1.009621)^{72}

So A > B

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...