Juan purchased an antique that had a value of $200 at the time of purchase. each year, the value of the antique is estimated to increase 10% percent over its value the previous year. the estimated value of the antique, in dollars, 2 years after purchase can be represented by the expression 200a, where a is a constant. what is the value of a?

The value of a is 1.21

Step-by-step explanation:

In order to obtain the value of a, you have to use The Exponential Growth Formula, because it represents a quantity increasing by a rate over a period of time, which is the given case.

The formula is:

Y: The amount of the quantity after the period of time

q:The initial quantity

r: The rate or percentage of growth

t: The period of time

In this problem:

q=200 dollars

r=10%=0.1 (As a decimal number)

t=2 years

Replacing the values of q,r and t:

But the value of Y was given as Y=200a, therefore:

Dividing by 200 both sides:

a=(1.1)²

a=1.21

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.