Mathematics: 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

Jane is saving her money in order to purchase

diana156

12.03.2022

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:

$C_1=3\times 2$

in next month the cost is:

$C_2=3\times 2\times 2\\\\C_2=3\times 2^2$

in t=3 months the expression is:

$C_3=3\times 2^2\times 2\\\\C_3=3\times 2^3$

Hence in general we say:

$C_t=3\times 2^t$

Hence,

$3\times 2^t=1536\\\\2^t=\dfrac{1536}{3}\\\\2^t=512\\\\2^t=2^9\\\\t=9$

Hence, option: D is true.

D) 3×(2)^t = 1,536; t = 9

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amylumey2005

16.04.2023

5x-6

Step-by-step explanation:

f(x) = 2x + 3

g(x) = 3x - 9

f(x) + g(x) = 2x + 3 + 3x-9

= 5x-6

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