Question

The new house at the end of the street was bought for $495,000. However, its value is going to go down at 2.4% each year. Which equation models this problem?

a. $495,000(0.976)^x
b. $495,000(0.024)^x
c. $495(2.4)^x
d. $495,000(1.024)^x

Shannon is 45 inches tall, and she is growing at a rate of 3% each month. Which equation models this problem?
a. 45(1.3)^x
b. 45(3)^x
c. 45(0.93)^x
d. 45(1.03)^x

The new phone you bought for $999 is losing 8% of its value each month. How much will it be worth in 2 years?
a. $845.55
b. $840
c. $1836.16
d. $900

A dog is about 16 cm long at birth. During the beginning of its life, the length increases by about 3% each week. How long is it after 10 weeks?
a. 164.8 cm
b. 21.5 cm
c. 4.8 cm
d. 23 cm

You put $100 in a bank account. It will grow at 2.5% each year. How much will it be worth in 30 years?
a. $200
b. $209.76
c. $74
d. $132.50

The new car you bought cost $27,000. It will depreciate at 11% each year. How much will the car be worth in 4 years?
a. $24,225.98
b. $40,987.90
c. $96,120
d. $16,940.41

Answer 1

The correct equations for depreciation and growth over time are essential for understanding how the value of belongings change. In the context of houses, cars, and personal growth, these values depend on the percentage change and the period of time considered. As such, specific equations can be used to model these scenarios correctly.

Step-by-step explanation:

The subject in question is Mathematics, specifically dealing with the decline or growth of values over time. This is a common topic in high school level algebra and finance education. In the given problems, the focus is on how the value of items like a house, car, and other investments change over time due to depreciation or growth rates. Here are the correct equations and calculations for each scenario:

• The equation for the depreciation of the house value at 2.4% per year is a. $495,000(0.976)^x.
• For Shannon's growth rate of 3% each month, the corresponding equation is d. 45(1.03)^x.
• The worth of a new phone after depreciation of 8% per month over 2 years is calculated as $999(0.92)^{24}, which would give an approximate value, not provided in the multiple choices.
• A dog growing at 3% each week for 10 weeks will have its length calculated as 16(1.03)^{10}, which results in approximately d. 23 cm.
• $100 in a bank account growing at 2.5% per year will be worth after 30 years calculated as $100(1.025)^{30}, which gives an approximate value, not provided in the multiple choices.
• The value of a car that depreciates by 11% each year after 4 years is calculated as $27,000(0.89)^4, resulting in d. $16,940.41 being the worth.