Stitz-Zeager_College_Algebra_e-book

6 we have observed that the more times you compound

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: to divide by ‘ln’. 6.3 Exponential Equations and Inequalities 359 1−x 1. Since 16 is a power of 2, we can rewrite 23x = 161−x as 23x = 24 . Using properties of exponents, we get 23x = 24(1−x) . Using the one-to-one property of exponential functions, we 4 get 3x = 4(1 − x) which gives x = 7 . To check graphically, we set f (x) = 23x and g (x) = 161−x and see that they intersect at x = 4 ≈ 0.5714. 7 2. We begin solving 2000 = 1000 · 3−0.1t by dividing both sides by 1000 to isolate the exponential which yields 3−0.1t = 2. Since it is inconvenient to write 2 as a power of 3, we use the natural log to get ln 3−0.1t = ln(2). Using the Power Rule, we get −0.1t ln(3) = ln(2), so we divide both sides by −0.1 ln(3) to get t = − 0.ln(2) = − 10 ln(2) . On the calculator, we graph 1 ln(3) ln(3) f (x) = 2000 and g (x) = 1000 · 3−0.1x and find that they intersect at x = − 10 ln(2) ≈ −6.3093. ln(3) y = f (x) = 23x and y = g (x) = 161−x y = f (x) = 2000 and y = g (x) = 1000...
View Full Document

Ask a homework question - tutors are online