Final answer:
The function h(x) = 1/8^x decreases as x increases from 7 to 10 because increasing the exponent in a fraction with a base larger than 1 results in a smaller overall value.
Step-by-step explanation:
To understand how the function h(x) = 1/8^x changes over the interval from x=7 to x=10, we should evaluate the function at these points and then compare the results. As x increases, the function's value, which is the outcome of a negative exponent, will decrease. This is because increasing the exponent in the denominator of a fraction makes the overall value smaller.
At x=7, we have:
h(7) = 1/8^7
At x=10, we have:
h(10) = 1/8^10
So as x increases from 7 to 10, h(x) decreases, because the base of the exponent (8) is greater than 1, making the value of 1/8^x get progressively smaller.