Question

Convert the function f(x) = 40e^(-0.35t) into the form f(x) = ab^(t).

A) f(x) = 40e^(-0.35t)
B) f(x) = 40(0.35)^t
C) f(x) = 40e^(-0.35)^t
D) f(x) = 40(2.718)^(-0.35t)

Answer 1

To convert the function f(x) = 40e^(-0.35t) into the form f(x) = ab^(t), express e in terms of a different base and simplify the equation.

Step-by-step explanation:

To convert the function f(x) = 40e^(-0.35t) into the form f(x) = ab^(t), we need to express the exponential function in terms of a different base. The given function is already in the form of f(x) = ae^(kt) where a = 40, e is the base of the natural logarithm, and k = -0.35. To convert it into the desired form f(x) = ab^(t), we need to express e in terms of a different base. The equivalent form using base 10 would be f(x) = 40(10^(-0.35))^t, which simplifies to f(x) = 40(0.447)^t. Therefore, the correct option is B) f(x) = 40(0.447)^t.