Is the question - did they mistakenly say "dollar" rather than "years?"
x = # of years
10,000 = 20,000 (0.85)^x, first divide both sides by 20,000
0.5 = (0.85)^x, next take the ln of both sides
ln 0.5 = ln (0.85)^x, by rules of logarithms you may move x to make it a coefficient of the logarithm
ln 0.5 = x (ln 0.85), divide both sides by ln (0.85)
x = (ln 0.5)/ (ln 0.85) = (-0.693)/(-0.1625) = 4.26 years
Answer:
Writing the inequality, we have;

the solution to the inequality is;

Explanation:
Given that Natalie has $680 to spend at a bicycle store for some new gear and biking outfits.
Total spending must not exceed $680

She buys a new bicycle for $383.33.
• She buys 2 bicycle reflectors for $7.61 each and a pair of bike gloves for $22.01.
She plans to spend some or all of the money she has left to buy new biking outfits
for $32.43 each.
let x represent the number of biking outfits she can buy.
Total spending is;

Writing the inequality, we have;

we can now solve the inequality;

Therefore, the solution to the inequality is;
Answer:
28,134 / 47 = 598.6
Step-by-step explanation: