n=250e^kt n=375 t=7, if n=750 what is t?

Question

Solve for T, using natural log please!!

Answer 1

n=250e^kt n=375 t=7

375 = 250e^7k

 

Solve for k initially to get the constant of proportion

 

375/250 = e^7k

Take ln of both sides

ln(375/250) = ln e^7k

ln(375/250) = 7k

 

k = [ln(375/250)]/7

k = .0579236

 

If n=750 what is t?

 

750 = 250e^.0579236t

 

750/250 = e^.0579236t

3 = e^.0579236t

ln3 = ln e^.0579236t

ln3 = .0579236t

 

t = ln3/.0579236

t = 18.9666

 

If you need to round this then t ≈ 19

 

 

Answer 2

If you meant a two part problem, where you solve for k in the first part and use that to find t for a different n, then:

 

First part:

 

375 = 250e^7k ⇒ k = ln(375/250) / 7 = 0.0579236

 

Second part:

 

Using k from the first part and n = 750,

 

750 = 250e^0.0579236T ⇒ T = ln(750/250) / 0.0579236 = 18.966575