Answer:
k ≈ 0.34
Step-by-step explanation:
Using the law of logarithms
log [tex]x^{n}[/tex] ⇔ nlogx
given N = [tex]N_{0}[/tex] [tex]e^{kt}[/tex]
Where [tex]N_{0}[/tex] is the initial amount
here N = 7500, t = 10 and [tex]N_{0}[/tex] = 250, hence
7500 = 250 [tex]e^{10k}[/tex] ( divide both sides by 250 )
[tex]e^{10k}[/tex] = 30 ( take the ln of both sides )
ln [tex]e^{10k}[/tex] = ln 30
10k lne = ln 30 [ lne = 1 ]
k = [tex]\frac{ln30}{10}[/tex] ≈ 0.34
