Question

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?

Answer 1

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

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