Question

mathematics 7 - 7 full year
←7: mathxl for school: practice & problem solving
part 2 of 3
a companys stock began the day at $34.02 per share. that price drops by $1.56 each hour.
a. what is the price per share after 5 hours?
b. what will it be after 23 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 5 hours?
a. the price per share after 5 hours is $26.22.
b. the price per share after 5 hours is -$2.11.
c. the price per share after 5 hours is -$1.86.
d. the price per share after 5 hours is $25.97.
b. what will it be after 23 hours if this rate continues?
a. the price per share after 23 hours will be $26.22.
b. the price per share after 23 hours will be -$2.11.
c. the price per share after 23 hours will be -$1.86.
d. the price per share after 23 hours will be $25.97.
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Explanation:

Step1: Determine the formula for stock - price

The initial price of the stock is $P_0 = 34.02$ dollars per share and it drops by $d = 1.56$ dollars per hour. The formula for the price $P$ after $t$ hours is $P=P_0 - dt$.

Step2: Calculate the price after 5 hours

Substitute $P_0 = 34.02$, $d = 1.56$, and $t = 5$ into the formula:
$P=34.02-1.56\times5=34.02 - 7.8=26.22$.

Step3: Calculate the price after 23 hours

Substitute $P_0 = 34.02$, $d = 1.56$, and $t = 23$ into the formula:
$P=34.02-1.56\times23=34.02-35.88=- 1.86$.

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 sense for the value of a stock share in the traditional way. It implies that based on the linear model of price - drop, the stock has dropped so much that it has a "negative value" which is a sign that the model may break down in the long - run as stock prices cannot be negative in reality.

Answer:

a. A. The price per share after 5 hours is $26.22.
b. C. The price per share after 23 hours will be $-1.86.
c. A positive answer for the stock - price means the stock still has value. A negative answer implies that, according to the linear model of price decrease, the stock has dropped below zero value, which is not possible in a real - world stock - pricing context and indicates the limitations of the simple linear model used for long - term prediction.