The amount of electricity that a solar panel is capable of producing slowly decays over time. After ten years, a solar panel produces 89% of the electricity that it was able to produce when it was brand new. Find the exponential decay constant k. If a solar panel is initially capable of producing 450 watts of power, how long will it take before the solar panel is only able to produce 300 watts of power?

It will take 34.79 years before the solar panel is only able to produce 300 watts of power

Step-by-step explanation:

The equation for the amount of electricity that a solar panel is capable has the following format:

In which Q(t) is the amount after t years, Q(0) is the initial amount and k is the exponential decay constant.

After ten years, a solar panel produces 89% of the electricity that it was able to produce when it was brand new.

This means that . So

So

Initially capable of producing 450 watts of power

This means that

How long will it take before the solar panel is only able to produce 300 watts of power?

This is t for which Q(t) = 300. So

It will take 34.79 years before the solar panel is only able to produce 300 watts of power

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap