Use guess and check to find when an exponential function with a decay rate of 7% per hour reaches half of its original amount, rounded up to the nearest hour. The exponential function reaches half of itsoriginal amount after how many hours?

The exponential function reaches half of its original amount after 4.08 hours.

Step-by-step explanation:

given information:

decay rate, λ = 17% = 0.17

reaches half of its original amount, N = 1/2 N₀

to calculate the time of decay, we can use the following formula

N = N₀e^ (-λt)

where

N = the amount left after the decay

N₀ = initial amount

λ = decay rate

t = time

thus,

N = N₀e^ (-λt)

1/2 N₀ = N₀ e^ (-0.17t)

1/2 = e^ (-0.17t)

ln (1/2) = - 0.17t

t = 4.08 hours