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Write an expression the value of a commodity after 20years if the value decrease at a monthly rate 2 ./. |
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Answer» ONG>ANSWER: ᴀ) ᴛʜᴇ ᴀɴsᴡᴇʀ ɪs ғ(ɴ) = 1500 * 0.8ⁿ ʟᴇᴛ ᴛʜᴇ ғᴜɴᴄᴛɪᴏɴ ʙᴇ ғ(ɴ) ᴡʜᴇʀᴇ ɴ ɪs ɴᴜᴍʙᴇʀ ᴏғ ʏᴇᴀʀs ᴀғᴛᴇʀ 20% ɪs ʟᴏsᴛ, ᴛʜᴇ ᴠᴀʟᴜᴇ ᴛʜᴀᴛ ʀᴇᴍᴀɪɴs ɪs 80% ᴏғ 1500: 1500 : 100% x : 80% 1500 : 100% = x : 80% x = 1500 * 80% : 100% x = 1500 * 80/100 x = 1500 * 0.8 ғᴏʀ ᴇᴀᴄʜ ʏᴇᴀʀ ᴡᴇ ᴍᴜsᴛ ᴀᴅᴅ ᴇxᴘᴏɴᴇɴᴛ, sᴏ ᴛʜᴇ ғᴜɴᴄᴛɪᴏɴ ɪs: ғ(ɴ) = 1500 * 0.8ⁿ ʙ) ᴛʜᴇ ᴀɴsᴡᴇʀ ɪs $768 ᴡᴇ ʜᴀᴠᴇ ғᴜɴᴄᴛɪᴏɴ: ғ(ɴ) = 1500 * 0.8ⁿ ᴀɴᴅ ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ ʏᴇᴀʀs ɪs 3: ɴ = 3 ғ(3) = 1500 * 0.8³ = 1500 * 0.512 = 768 ᴄ) ᴛʜᴇ ᴀɴsᴡᴇʀ ɪs 5 ʏᴇᴀʀs ᴡᴇ ʜᴀᴠᴇ ғᴜɴᴄᴛɪᴏɴ: ғ(ɴ) = 1500 * 0.8ⁿ ᴀɴᴅ ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ᴛʜᴇ ᴠᴀʟᴜᴇ ɴᴇᴇᴅs ᴛᴏ ʙᴇ ʟᴇss ᴛʜᴇɴ $500: ғ(ɴ) = <500 1500 * 0.8ⁿ < 500 0.8ⁿ < 500 / 1500 0.8ⁿ < 0.33 ʟᴏɢ(0.8ⁿ) < ʟᴏɢ(0.33) ɴ * ʟᴏɢ(0.8) < ʟᴏɢ(0.33) ɴ * -0.0969 < -0.4815 ɴ < -0.4815 / -0.0969 ɴ < 5 |
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