select the correct answer.\njane planted a marigold sapling in her garden and recorded its growth every…

select the correct answer.\njane planted a marigold sapling in her garden and recorded its growth every week. the plants height, in inches, is modeled by the function (h(x)), where (x) is the number of weeks since jane planted the sapling.\n| (x) | (h(x)=3sqrt{7x + 1}) |\n| ---- | ---- |\n| 0 | 3 |\n| 1 | 8.49 |\n| 2 | 11.62 |\n| 3 | 14.07 |\n| 4 | 16.16 |\n| 5 | 18 |\nwhat is true of the function as the (x)-values increase?\na. the function is increasing, but the average rate of change is decreasing.\nb. the function is increasing, and the average rate of change is increasing.\nc. the function is decreasing, but the average rate of change is increasing.\nd. the function is decreasing, and the average rate of change is decreasing.

select the correct answer.\njane planted a marigold sapling in her garden and recorded its growth every week. the plants height, in inches, is modeled by the function (h(x)), where (x) is the number of weeks since jane planted the sapling.\n| (x) | (h(x)=3sqrt{7x + 1}) |\n| ---- | ---- |\n| 0 | 3 |\n| 1 | 8.49 |\n| 2 | 11.62 |\n| 3 | 14.07 |\n| 4 | 16.16 |\n| 5 | 18 |\nwhat is true of the function as the (x)-values increase?\na. the function is increasing, but the average rate of change is decreasing.\nb. the function is increasing, and the average rate of change is increasing.\nc. the function is decreasing, but the average rate of change is increasing.\nd. the function is decreasing, and the average rate of change is decreasing.

Answer

Answer:

A. The function is increasing, but the average rate of change is decreasing.

Explanation:

Step1: Check function trend

As (x) goes from (0) to (5), (h(x)) values (3, 8.49, 11.62, 14.07, 16.16, 18) are increasing. So the function is increasing.

Step2: Calculate average rate of change

For (x = 0) to (x = 1), average rate of change (=\frac{h(1)-h(0)}{1 - 0}=\frac{8.49 - 3}{1}=5.49). For (x = 4) to (x = 5), average rate of change (=\frac{h(5)-h(4)}{5 - 4}=\frac{18 - 16.16}{1}=1.84). Since (5.49>1.84), the average rate of change is decreasing.