Question 41298
Costs on vehicles is a great example! Vehicles constantly decline in cost because they are constantly being used.
If you bought a really cheap car at $1000.00 and it declined at a rate of 3%, then you have a logarithmic equation:
{{{P(a) = a(1 - r)^t}}}
{{{P(a) = 1000(1 - 0.03)^t}}}
{{{P(a) = 1000(0.97)^t}}}
When will the car be worth $900.00?
{{{900 = 1000(0.97)^t}}}
{{{0.9 = (0.97)^t}}}
{{{log(10,0.9) = log(10,(0.97)^t)}}}
{{{log(10,0.9) = t*log(10,(0.97))}}}
{{{log(10,0.9)/log(10,(0.97)) = t}}}
About 3.5 years
To graph it:
{{{P(a) = 1000(0.97)^x}}} change the {{{t}}} to {{{x}}} for the x-axis to be time
{{{ graph( 500, 650, -1, 10, -16, 1000, 1000(0.97)^x, 900) }}}