Suppose a long term investment is modeled by the exponential function v(t) = 30(25)t/20 where v(x) is the total value after t year. what does 25 represent in equation?
a. the interest rate
b. the growth factor
c. the initial deposit
d. the number of years

Option: b is the correct answer.

b.  The growth factor

Step-by-step explanation:

We are given a expression that represents the investment made.

The  long term investment is modeled by the exponential function:

where,

V(t) is the total value after t year.

The constant '25' here represents the growth factor by which our value is increasing each year.

constant '30' represents the initial value i.e. the investment made.

Hence, option: b is the correct answer.

b. The growth factor

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4