A new automobile costs $32,000. The value of the same automobile after t years is given by V = 32000(0.8)t. The following steps determine how many years it will take for the value to decrease to one-eighth the initial value, which is $4,000.

 

1) we need to compute (0.8)t = 1/8, so we take logarithm of base 10 on both side: write out the result.

 

2) using the fact that log102 = 0.3010, compute log108. [hint: 23 = 8]

 

3) use the result of log108, compute log10(1/8). [hint: 1/8 = 8-1]

 

4) use the result of log108, compute log100.8 [hint: 0.8 = 8/10]

 

5) use the result of 3) and 4), solve for t in 1)

 

Homework #5A new automobile costs $32,000. The value of the same automobile after t yearsis given by V = 32000(0.8)t. The following steps determine how many years it willtake for the value to decrease to one-eighth the initial value, which is $4,000.1) we need to compute (0.8)t= 1/8, so we take logarithm of base 10 on bothside: write out the result.2) using the fact that log102 = 0.3010, compute log108. [hint: 23= 8]3) use the result of log108, compute log10(1/8). [hint: 1/8 = 8-1]4) use the result of log108, compute log100.8 [hint: 0.8 = 8/10]5) use the result of 3) and 4), solve for t in 1)Reminder: homework turned in before or on the speciFed due date and time, inclass or submitted through Blackboard, depending on the circumstance, areeligible for 100% of the grade. If you choose to turn in after the due date and timepasses, for the Frst 24 hour period after the due date and time, your assignmentwill be eligible for 67% of the full grade; for the second 24 hour period after thedue date and time, your assignment will be eligible for 33% of the full grade; forthe third 24 hour period or later after the due date and time, your assignment willbe eligible for 0% of the full grade.1

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