Question

Convert the equation f ( t ) = 199 e 0.04 t to the form f ( t ) = a b t

Answer 1

To convert the function f(t) = 199e^0.04t to the form f(t) = ab^t, recognize that e is the constant 2.71828, thus the function can be rewritten as f(t) = 199(2.71828)^0.04t.

Step-by-step explanation:

The student has asked to convert the exponential function f(t) = 199e0.04t to the form f(t) = abt. To convert this, remember that the base e is a constant approximately equal to 2.71828. So, if we have an expression like ex, we can rewrite this as (2.71828)x. In this case, we have e0.04t, which can be rewritten as (2.71828)0.04t. Therefore, the given function can be rewritten as f(t) = 199(2.71828)0.04t, which is now in the desired form.