Question

The value of a mountain bike Y(in dollars) can be approximated by the model Y=200(1-.0025) to the t power, where T is the number of years since the bike was new. Estimate when the bike will be $50.

Answer 1

It will take 554 years

Explanation:

Here, we want to estimate the time when t will be $50

We can rewrite the exponential equation as;

y = 200(1-0.0025)^t

In this case, y = $50 and we want to calculate t

so, we simply proceed to substitute the value 50 for y

we have this as ;

50 = 200(1-0.0025)^t

50/200 = (1-0.0025)^t

1/4 = 0.9975^t

0.25 = 0.9975^t

Take the natural logarithm of both sides

ln 0.25 = ln 0.9975^t

ln 0.25 = t ln 0.9975

t = ln 0.25 / ln 0.9975

t = 553.8 = 554 years

The bike will be $50 in 554 years