Question

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. The bike Jane wants is $1,536 at the local bike shop.

Which equation represents this situation, and after how many months, t, will Jane have enough money to purchase the bike?

A, 3(2)t = 1,536; t = 11
B, 3(1.2)t = 1,536; t = 35
C, (3 · 2)t = 1,536; t = 9
D, 3(2)t = 1,536; t = 9

Answer 1

the Answer is D)
i just did the math. plug 3(2)^9 in to a calculator!

Answer 2

Hence, option: D is true.

D) 3×(2)^t = 1,536; t = 9

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:

`C_1=3* 2`

in next month the cost is:

`C_2=3* 2* 2\\\\C_2=3* 2^2`

in t=3 months the expression is:

`C_3=3* 2^2* 2\\\\C_3=3* 2^3`

Hence in general we say:

`C_t=3* 2^t`

Hence,

`3* 2^t=1536\\\\2^t=(1536)/(3)\\\\2^t=512\\\\2^t=2^9\\\\t=9`

Hence, option: D is true.

D) 3×(2)^t = 1,536; t = 9