Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y = 980(1.08)

6.67 m

Step-by-step explanation:

Hello!

This is a similar triangles problem. There are different ways to approach this. We could use angles, but that involves trig. An easier way is to use ratios.

First, let's look at the picture. There are two triangles, one that has a length of 1.5 m and a height of 2 m, and a larger triangle, with a length of 5 m and a height of n m. We can relate these triangles and their lengths/heights because they are similar triangles.

So, if there are 2 triangles, we can relate

where and are the length and height of the first triangle and and are the length and height of the second triangle.

So, let's apply it:

Okay, and solve for the unknown, n:

So, we found n = 6.66667 or, rounded to the nearest hundreth as the instructions state, 6.67 m. Since it's one of the listed options, that indicates we're correct. However, we should also apply a "does this make sense check": does 6.67 make sense as an answer?

Well, the length for the smaller triangle are 1.5 and 2.  Those values are very close to eachother. So are 5 and 6.67. So our answer does make sense! We could also check our work by substituting 6.67 for n in our original ratio and evaluate each side of the equal sign:

Yep! Through this check, we can show that our answer is correct!