Question

a companys stock began the day at $30.50 per share. that price drops by $1.05 each hour.
a. what is the price per share after 6 hours?
b. what will it be after 32 hours if this rate continues?
c. explain what the signs of the answers mean in this context.
a. what is the price per share after 6 hours?
a. the price per share after 6 hours is $24.20.
b. the price per share after 6 hours is -$2.50.
c. the price per share after 6 hours is $24.45.
d. the price per share after 6 hours is -$2.84.
b. what will it be after 32 hours if this rate continues?
a. the price per share after 32 hours will be $24.45.
b. the price per share after 32 hours will be -$2.50.
c. the price per share after 32 hours will be $24.20.
d. the price per share after 32 hours will be -$2.84.

Explanation:

Step1: Determine the formula for stock - price calculation

The initial price of the stock is $P_0 = 30.50$ and it drops by $d = 1.01$ each hour. The formula for the price $P$ after $t$ hours is $P=P_0 - d\times t$.

Step2: Calculate the price after 6 hours

Substitute $P_0 = 30.50$, $d = 1.01$, and $t = 6$ into the formula: $P=30.50-1.01\times6$. First, calculate $1.01\times6 = 6.06$. Then, $P=30.50 - 6.06=24.44$.

Step3: Calculate the price after 32 hours

Substitute $P_0 = 30.50$, $d = 1.01$, and $t = 32$ into the formula: $P=30.50-1.01\times32$. First, calculate $1.01\times32 = 32.32$. Then, $P=30.50 - 32.32=- 1.82$.

Step4: Interpret the signs

A positive price means the stock still has value. A negative price in this context is not possible in a real - world stock - trading sense immediately, but it implies that the stock has dropped so much in value that if the trend continued, the value of the stock has gone below zero (which may indicate significant financial distress for the company).

Answer:

a. C. The price per share after 6 hours is $24.44$ (closest to the calculated value among the options, there may be a rounding difference in the options).
b. D. The price per share after 32 hours will be - $1.82$ (closest to the calculated value among the options, there may be a rounding difference in the options).
c. A positive answer for the stock - price means the stock still has a non - zero value. A negative answer implies that if the downward trend continued, the stock's value has dropped below zero, which is an indication of severe financial problems for the company in a real - world context, although negative stock prices are not common in normal trading scenarios as stocks represent ownership and typically have at least some residual value.