Question

mr. olsen, the owner of trading card depot, purchased a rare baseball card valued at $98.70. he expects the card’s value to double each year. write an exponential equation in the form ( y = a(b)^x ) that can model the card’s value, ( y ), in dollars, ( x ) years after mr. olsen purchased it. use whole numbers, decimals, or simplified fractions for the values of ( a ) and ( b ). ( y = ) what can mr. olsen expect the card’s value to be 5 years after he purchased it? $ submit

Explanation:

Step1: Identify initial value (a)

The initial value of the card is the purchase price, so $a = 98.70$.

Step2: Identify growth factor (b)

The value doubles each year, so the growth factor $b = 2$.

Step3: Write exponential equation

Substitute $a$ and $b$ into $y=a(b)^x$.
$y = 98.70(2)^x$

Step4: Calculate value at x=5

Substitute $x=5$ into the equation.
$y = 98.70(2)^5 = 98.70 \times 32$

Step5: Compute final value

Calculate the product.
$98.70 \times 32 = 3158.40$

Answer:

$y = 98.70(2)^x$
$3158.40$