Answer:
Explanation:
If Daniel has data represented by the exponential function f(x) = 2x, where x is the number of mosquitoes, he can convert this equation to a logarithmic function when the temperature is 64 degrees by following these steps:
Substitute the value of the temperature into the function: f(x) = 2x becomes 64 = 2x.
Take the logarithm of both sides of the equation with base 2: log₂(64) = log₂(2x).
Use the properties of logarithms to simplify the right side of the equation: log₂(64) = x * log₂(2).
Since log₂(2) = 1, we can simplify further: log₂(64) = x.
Evaluate log₂(64) to find the value of x: log₂(64) = 6, so x = 6.
So, when the temperature is 64 degrees, the logarithmic function that represents the data is log₂(64) = x, or x = log₂(64). This means that when the temperature is 64 degrees, there are approximately 6 mosquitoes.