Cate purchases $1600 worth of stock and her broker estimates it will increase in value by 4.2% each year. after about how many years will the value of cate’s stock be about $2000?

Since the money appreciates 4.2% each year, then:

2000=1600x(1.042)^n, where n is the number of years

Then:

1.25=1.042^n

ln 1.25=ln 1.042^n=n ln 1.042

n=5.424 years

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."