A function g(t) decreases by a factor of 6 over every unit interval in t and g(0)=3.Which could be a function rule for g(t)?

The function g(t) is decreasing by a factor of 6 over every unit interval in t. This suggests that the function is an exponential decay function, which can be written in the form g(t) = ab^t, where a is the initial value and b is the decay factor.

Given that g(0) = 3, we can substitute these values into the function to find the initial value a.

g(0) = ab^0 3 = a*1 a = 3

The function decreases by a factor of 6 over every unit interval in t, which means the base b of the exponential function is 1/6 (since it's decreasing).

So, a possible function rule for g(t) could be:

g(t) = 3*(1/6)^t