Asubstance decays so that the amount a of the substance left after t years is given by: a = a 0 · (0.75) t , where a 0 is the original amount of the substance. what is the amount of time it takes for there to be one-third of this substance left, rounded to the nearest tenth of a year?

Let  be the original amount of the substance. After t years, the amount left A is given by:

                               .

For example, after 1 year, the amount is

      .

Thus, after one year, only 0.75=3/4 of the original amount is left.

We want to solve for t, such that   is one-third of , so we set the equation:

.

Simplifying by , we have:

.

This is an exponential equation, so we can solving it by rewriting it as a logarithm:

.

3.8

Do the math. she originally had 50 dollars on her gift card and she had 12 dollars left on her gift card after she finished her shopping spree. if you subtract 50 minus 12 you get thirty eight dollars as your answer. so therefore, ciara spent 38 dollars total o

The variables should add up to equal 1