The selling price of a certain collector’s item was $10 in 2000 and $15 in 2001. If the selling price of the item follows a geometric sequence, what would the price of the item be in 2002?

The price of the item in 2002 would be $22.5

Step-by-step explanation:

Recall that the nth term of a geometric sequence of first term (in our case $10), is given by the formula:

where "r" is the common ratio obtained by the quotient of a term of the sequence divided by the previous term. In this case such common ratio is given by the quotient of $15 divided the previous value $10,

That is:

Then the price of the item in the year 2002 (which is the third term of the sequence; n = 3) is given by:

That is, the price of the item would be $22.5

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2