Tree A is curved which means it could be an exponential function. The yy-coordinates are 10, 20, 40, and 80. Since the yy-coordinates are doubling every 10 years, then the function is exponential since exponential functions have a constant factor (the number you multiply by).
2. Unlike the yy-coordinates for Tree A, the yy-coordinates for Tree B are not increasing by a constant factor. Since
Exponential functions are of the form
Linear functions are of the form
From the previous problems, Tree A is growing by a constant factor of 2 every 10 years and Tree B is growing by a constant amount of 25 feet every 10 years. In the long term, Tree A has a greater growth rate than Tree B since growing by a constant factor will give greater increases than growing by a constant amount as time increases.
5. From the graph, the initial height of Tree A was 10 feet in 1960. From the table, the initial height of Tree B was 12 feet in 1960. Therefore, Tree B had a greater initial height.
6. From the graph and table, in 1990 Tree A had a height of 80 feet and Tree B had a height of 87 feet. Tree A's height will then exceed Tree B's height sometime after 1990. Since 1990 is 30 years after 1960, then
The height of Tree A will then exceed the height of Tree B after