Jacob consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Jacob's body decreases exponentially. The 10-hour decay factor for the number of mg of caffeine in Jacob's body is 0.2601.

Answer: 0.87400mg of caffeine.

Step-by-step explanation:

You have

N (t) = N0 (e^-rt) (1)

as a general Exponential decay equation where N0 is the amount at t=0, N (t) is the amount remaining at time t and r is the exponential decay constant. You're specifically given that after 10 hours, the decay factor is 0.2601, i. e.,

N (10) / N (0) = N0 (e^-10r) / N0 (e^0) = e^-10r=0.2601 ... (2)

Taking the last 2 parts of (2) to the power of 0.1t gives

e^-rt=0.2601^.1t ... (3)

This means that

N (t) = N0 (e^-rt) = N0 (0.2601^.1t) ... (4)

Also,

N (2.56) N (1.56) = N0 (0.2601.1 (2.56)) N0 (0.2601.1 (1.56)) = 0.2601.1 (2.56-1.56) = 0.2601^.1

= 0.87400mg of caffeine.