Question

What is the function t written as a function of V, given that the investment value V is defined by V = 16(0.08)^t?

Answer 1

To express t as a function of V given V = 16(0.08)^t, rearrange the equation to find t = log(V/16) / log(0.08).

Step-by-step explanation:

The question is asking to solve for the function t as a function of the investment value V, given that the investment value V is defined by the formula V = 16(0.08)^t. To find t as a function of V, we need to rearrange this equation. Let's solve it step by step:

1. Start with the equation: V = 16(0.08)^t.
2. Divide both sides of the equation by 16: V/16 = (0.08)^t.
3. Take the logarithm of both sides to get t out of the exponent, using the property that log(a^b) = b*log(a): log(V/16) = t*log(0.08).
4. Divide both sides by log(0.08) to isolate t: t = log(V/16) / log(0.08).

Thus, we have t as a function of V expressed as t = log(V/16) / log(0.08).