The isotope Herodium-100 decreases by half every minute, Herodium-100 is there isotope that gives a super hero their strength. Once the amount depletes to 4 ml, a
superhero becomes tired and need to leave the fight. If Mathman has 2000mL in his
body, when will he have to rest and replenish, rounded to the nearest minute?

After about 9 minutes.

Step-by-step explanation:

We can write an exponential function to model the decay of Herodium-100.

We are given that it decreases by half every minute.

The standard exponential function is given by:

Where A is the initial amount, r is the rate, and m is the rate (in this case, in minutes).

Mathman initially has 2000 mL of Herodium-100. Therefore, A = 2000.

And since it decreases by half every minute, r = 1/2. Thus:

Mathman needs to rest when the Herodium-100 levels drop to 4 mL. Therefore, we can substitute 4 for f(m) and solve for m:

Solve for m. Divide both sides by 2000:

We can take the natural log of both sides:

By logarithm properties:

Therefore:

Mathman will have to rest and replenish after 9 minutes.

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