Question

Determine the exponential function that satisfies the given conditions, where the initial mass is 0.6 g, and the quantity is doubling every 3 days.

Which of the following expressions represents the exponential function?
a) 0.6×3
b) 0.63ˣ
c) 0.63/x
​d 0.63x/0.6
​

Answer 1

The correct exponential function for a quantity starting at 0.6 grams and doubling every 3 days is f(t) = 0.6 × 2^(t/3), where 't' is the time in days. None of the given options match this function exactly, but option b) might represent the correct answer if a typo occurred in the options.

Correct option is b)

Step-by-step explanation:

We need to determine the exponential function that represents a quantity starting at 0.6 grams and doubling every 3 days. In general, an exponential function has the form f(t) = a × bt, where 'a' is the initial amount, 'b' is the growth factor, and 't' is the time in days.

Since the initial amount is 0.6 grams, 'a' is 0.6. The quantity doubles every 3 days, so the growth factor 'b' is 2 (since doubling means multiplying by 2), and 't/3' represents the number of 3-day intervals that have passed.

The correct exponential function is f(t) = 0.6 × 2t/3. None of the given options precisely match this, but using properties of exponents, we can say that f(t) = 0.6 × 2t/3 = 0.6 × (21/3)t = 0.6 × 21/3×t, which is not listed explicitly in the options provided. If a typographical error has occurred and option b) was meant to be 0.6 × 2t/3, then it would be the correct representation of the exponential function.