Building a is 271 meters taller than building b. if the height of building a is subtracted from twice the height of building b, the result is 211 meters. how tall is each skyscraper?

Let a and b represent the heights of the corresponding buildings (in meters).

... a = b +271 . . . . . . . a is 271 meters taller than b

... 2b -a = 211 . . . . . . if a is subtracted from twice b, the result is 211

Use the expression for a in the first equation to substitute for a in the second.

... 2b - (b+271) = 211

... b = 482 . . . . . . . . . . . simplify and add 271

... a = b +271 = 753

Building a is 753 meters tall; building b is 482 meters tall.

The multiplicative rate of change of the function is 0.5

Explanation:

The multiplicative rate of change is the ratio between consecutive entries.

Naming r the multiplicative rate of change, if it is constant you get:

r = second entry / first entry = third entry / second entry = fourth entry / third entry.

Here:

second entry / first entry = 0.125 / 0.25 = 0.5third entry / second entry = 0.0625 / 0.125 = 0.5fourth entry / third entry = 0.03125 / 0.0625 = 0.5

Thus, the multiplicative rate of change is 0.5. It means that you can obtain each entry as the product of the previous entry times 0.5:

0.25 × 0.5 = 0.1250.125 × 0.5 = 0.06250.0625 × 0.5 = 0.03125

In general, exponential functions have constant multiplicative rate of changes.