+73 For each problem below, solve algebraically. Then, use a table or graph to check your answer.
+129849 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
