A 30-year-old woman has an average bone tissue density of 1.8 g/cm³ with an estimated bone tissue volume of 5,000 cm³. Assuming her bone tissue volume remains the same, what will her bone tissue density be if she is expected to lose 1.5 kg of bone mass by age 70 due to osteoporosis?

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11ecba2d_1301_9cca_a3bf_5748603aef44_MD0008_00 The density of an object represents the amount of mass contained in a unit of volume, and it has SI units of kg/m³. The woman's bone tissue density ρ is calculated as her bone mass m divided by her bone volume V: 11ecba2d_1301_9ccb_a3bf_0faf2766368f_MD0008_00 The above equation can be rearranged to solve for m. Therefore, her bone mass at age 30 is the product of her bone density at age 30 (1.8 g/cm³) and her bone volume (5,000 cm³): 11ecba2d_1301_9ccc_a3bf_81cf20e97ad8_MD0008_00 11ecba2d_1301_9ccd_a3bf_0b6c7dbdcd72_MD0008_00 At age 70, the woman's bone mass is expected to decrease by 1.5 kg. This value is converted to grams using the unit conversion 1 kg = 1,000 g to determine her new bone mass at age 70: 11ecba2d_1301_9cce_a3bf_6966fc4c4a65_MD0008_00 11ecba2d_1301_c3df_a3bf_19a0e7e283a5_MD0008_00 Assuming the woman's bone volume remains the same, her bone density at age 70 is calculated using V = 5,000 cm³ and her new bone mass (7,500 g): 11ecba2d_1301_c3e0_a3bf_4944a93be78a_MD0008_00 (Choice A) Density is calculated as mass divided by volume. If instead the woman's bone volume (5,000 cm³) is divided by her bone mass (7,500 g), the result is 0.67 cm³/g, which is the inverse of density. (Choice B) The woman's bone volume is given and assumed to be unchanged. If her bone volume is incorrectly calculated as her bone density (1.8 g/cm³) divided by her expected loss in bone mass (1.5 kg), the result is 1.2 g/(kg⋅cm³), which has units of inverse volume. (Choice D) The woman's bone density at age 70 is expected to decrease because her bone volume remains unchanged while her bone mass decreases by 1.5 kg. If her bone mass at age 70 is determined by incorrectly adding 1.5 kg, her bone density is calculated as 2.1 g/cm³. Educational objective: The density ρ of an object is its mass m divided by its volume V: ρ = m/V. This equation can be used to determine an object's mass from density and volume.

A 30-Year-Old Woman Has an Average Bone Tissue Density of 1.8