For each problem below, solve **algebraically**. Then, use a table or graph to check your answer.

GAMEMASTERX40 Apr 7, 2019

#1**+1 **

2)

a) The function is

H(t) = 540(1 +.039)^t

b) In 1999...t = 4.....so we have

H(4) = 540(1 + .039)^4 ≈ 629 houses in 1999

c) We need to solve this for t

1000 = 540 (1.039)^t divide both sides by 540

(1000/540) = 1.039^t take the log of both sides

log (1000/540) = log 1.09^t and, by a log property, we can write

log(1000/540) = t * log(1.039) divide b oth sides by log 1.039

log(1000/540) / log (1.039) = t ≈ 16 years (after 1995)

So 1000 houses will be reached in 1995 + 16 ≈ 2011

Here's the graph : https://www.desmos.com/calculator/pwt0jwnfxy

CPhill Apr 7, 2019