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

 Apr 7, 2019
 #1
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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

 

 

cool cool cool

 Apr 7, 2019
edited by CPhill  Apr 7, 2019

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