number of year, x | value of the antique, y\n0 | $7,196\n1 | ?\nif the value of an antique increases at a…

number of year, x | value of the antique, y\n0 | $7,196\n1 | ?\nif the value of an antique increases at a rate of 9% each year, what is the value after 1 year?\n○ $7,843.64\n○ $7,205\n○ $13,672.40\n○ $7,187

number of year, x | value of the antique, y\n0 | $7,196\n1 | ?\nif the value of an antique increases at a rate of 9% each year, what is the value after 1 year?\n○ $7,843.64\n○ $7,205\n○ $13,672.40\n○ $7,187

Answer

Explanation:

Step1: Identify the formula for growth

The formula for exponential growth is ( y = a(1 + r)^x ), where ( a ) is the initial value, ( r ) is the growth rate, and ( x ) is the time. Here, ( a = 7196 ), ( r = 0.09 ) (since 9% = 0.09), and ( x = 1 ).

Step2: Substitute the values into the formula

Substitute ( a = 7196 ), ( r = 0.09 ), and ( x = 1 ) into ( y = a(1 + r)^x ):
( y = 7196(1 + 0.09)^1 )
Simplify ( 1 + 0.09 = 1.09 ), so ( y = 7196 \times 1.09 ).

Step3: Calculate the product

Calculate ( 7196 \times 1.09 ):
( 7196 \times 1.09 = 7196 + 7196 \times 0.09 )
( 7196 \times 0.09 = 647.64 )
( 7196 + 647.64 = 7843.64 ).

Answer:

$7,843.64