Step-by-step explanation:

 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

Answer:

[

[tex]= \geqslant \pink{rate = 2\% \: monthy = 24 \: yearly \: = time = 20 \: years}[/tex]

[tex] \: \: \\ to \: find \: \orange{ = \geqslant } \: expression \: for \: value \: of \: commodity

[/tex]

[tex] = \geqslant cos \: = \: p \: \infty (1 - \frac{r}{100}) [/tex]

[tex] = > p \: \infty (1 - \frac{24}{100}) {}^{20} [/tex]

[tex] = \geqslant p \: \infty = (\frac{76}{100} ) {}^{20} [/tex]

[tex] = > p \: \infty \: ( \frac{19}{25} ) {}^{20} [/tex]

[tex]so \: answer = \geqslant \\ values \: of \: commodity \: be \: = p \: \infty (\frac{19}{25}) {}^{20} [/tex]