exponential decay to natural exponential decay equation

Question

if P=176(0.7)^t   and I have to put it in P=P₀e^kt 

How can I find k? 

 

Note: I know that P₀=176

Answer 1

P(t) = 176 (0.7)^t

 

P(t) = P₀e^kt = 176e^kt

 

Set these 2 equal to each other and solve for k:

 

176 (0.7)^t = 176 e^kt

 

(0.7)^t = e^kt

 

Take ln of both sides:

 

t ln(0.7) = kt

 

k = ln(0.7) ≅ -0.356675

 

P(t) ≅ 176 e^{-0.356675 t}