Question 1155437
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It's not clear what help you are asking for....<br>
The easiest way to solve problems like these is with a graphing calculator.<br>
For the first problem, graph the functions {{{2200(0.98^x)}}} and {{{1500}}} and find their point of intersection.<br>
{{{graph(400,400,-10,30,-500,2500,2200(0.98^x),1500)}}}<br>
Algebraically,<br>
{{{2200(0.98^x) = 1500}}}
{{{0.98^x = 1500/2200 = 15/22}}}
{{{x*log((0.98)) = log((15/22))}}}
{{{x = log((15/22))/log((0.98))}}} = 18.96 to 2 decimal places<br>
ANSWER: It will take 19 months for the value to drop below $1500.<br>
For the second problem about half lives, the formula is<br>
{{{y = A(1/2)^x}}}<br>
where x is the number of half-lives.  For your problem,<br>
{{{150(1/2)^x = 100}}}<br>
Again the easiest solution is with a graphing calculator.<br>
{{{graph(400,400,-1,2,-50,200,150(.5^x),100)}}}<br>
Algebraically,<br>
{{{150(1/2)^x = 100}}}
{{{(1/2)^x = 100/150 = 2/3}}}
{{{x*log((1/2)) = log((2/3))}}}
{{{x = log((2/3))/log((1/2))}}} = 0.585 to 3 decimal places.<br>
ANSWER: It will take about 0.585 half lives, or 0.585*27 = 15.8 days, for the amount to drop to 100g.<br>