Convert the equation f (t) = 190 (1.33) ^t to the form f (t) = ae^kt

a=

k=

Give values accurate to three decimal places

a = 190

k = 0.285

Step-by-step explanation:

f (t) = 190 (1.33) ^t

At t = 0, f (t) = 190. So a = 190.

f (t) = 190 e^ (kt)

Set equal and solve for k:

190 (1.33) ^t = 190 e^ (kt)

1.33^t = e^ (kt)

ln (1.33^t) = kt

t ln (1.33) = kt

k = ln (1.33)

k = 0.285