Question

A point moves along a straight path. The function f(t) = log3(t) determines the distance (in meters) the point has traveled in terms of the number of seconds t since the point started moving. What is the distance traveled by the point after 5 seconds?

Answer 1

The distance traveled by the point after 5 seconds is determined by evaluating the logarithmic function f(5) = log3(5). This can be done using a calculator, or the change of base formula. The result gives the total distance traveled in meters.

Step-by-step explanation:

The distance traveled by the point after 5 seconds can be found by evaluating the function f(t) = log3(t) at t = 5. Plugging in the value, we get f(5) = log3(5). This will give us the distance in meters the point has traveled after 5 seconds.

To calculate this, you can use a calculator that allows you to compute logarithms with various bases, or use the change of base formula which states that logb(a) = logc(a) / logc(b), where c can be any positive number. Using the common logarithm (base 10), the distance is computed as f(5) = log(5)/log(3).

After solving the expression, we can find the numerical value representing the total distance traveled by the point.