4 For each situation below, decide whether it is linear or exponential and write

Question

4 For each situation below, decide whether it is linear or exponential and write an equation using the variables given. (For this question, you do not need to solve the equation or answer the question being asked.) If the equation is linear, explain how m and b can be found in the situation. If it is exponential, explain how cand a occur in the situation a. The height of a tree grows from 20 inches when it was planted to 75 inches 6 years later. If it grows the same amount each year when will it be 100 inches? Let h be the height of the tree x years after it was planted. b. Forest Ranger found there was a connection between the increase in human population in an area and the decrease in the population of deer. During a certain period the human population increased 12% a year and the deer population decreased 14% a year over the same period. The deer population started at 243 and if the trend continues, after how many years will the deer population be less than 10? Let d be the deer population y years after the start of the study

Explanation / Answer

a. linear equation

The height increased after planting the tree in 6years is 75-20=55

so m =(75-20)/6

b=20 initial height of a plant

h=my+b

100=(55/6)×y+20

y=96/11

b. exponential equation

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