Answer:
Hence, option: D is true.
D) 3×(2)^t = 1,536; t = 9
Step-by-step explanation:
Jane is saving her money in order to purchase a new racing bike. She initially saves $3 and plans to double the amount she saves each month.
he bike Jane wants is $1,536 at the local bike shop.
The equation that represents this situation, and after how many months, t, will Jane have enough money to purchase the bike is:
D) 3×(2)^t = 1,536; t = 9
since in the first month the cost is:
[tex]C_1=3\times 2[/tex]
in next month the cost is:
[tex]C_2=3\times 2\times 2\\\\C_2=3\times 2^2[/tex]
in t=3 months the expression is:
[tex]C_3=3\times 2^2\times 2\\\\C_3=3\times 2^3[/tex]
Hence in general we say:
[tex]C_t=3\times 2^t[/tex]
Hence,
[tex]3\times 2^t=1536\\\\2^t=\dfrac{1536}{3}\\\\2^t=512\\\\2^t=2^9\\\\t=9[/tex]
Hence, option: D is true.
D) 3×(2)^t = 1,536; t = 9
