Lana follows a recipe to make muffins. She finds they are too sweet, so in the next batch, she uses three-fourths as much sugar. She continues refining the recipe by using three-fourths as much sugar in each successive batch. If she used 500 grams of sugar in the first batch, which expression can Lana use to find the total number of grams of sugar she will use to make the first 6 batches of muffins?

Question

Lana follows a recipe to make muffins. She finds they are too sweet, so in the next batch, she uses three-fourths as much sugar. She continues refining the recipe by using three-fourths as much sugar in each successive batch. If she used 500 grams of sugar in the first batch, which expression can Lana use to find the total number of grams of sugar she will use to make the first 6 batches of muffins?

(1 point)
Responses

start fraction 500 times left parenthesis 1 minus left parenthesis three fourths right parenthesis superscript 6 baseline right parenthesis end fraction
Image with alt text: start fraction 500 times left parenthesis 1 minus left parenthesis three fourths right parenthesis superscript 6 baseline right parenthesis end fraction

start fraction 500 times left parenthesis 1 minus three fourths right parenthesis over left parenthesis 1 minus three fourths right parenthesis end fraction
Image with alt text: start fraction 500 times left parenthesis 1 minus three fourths right parenthesis over left parenthesis 1 minus three fourths right parenthesis end fraction

start fraction 500 times left parenthesis 1 minus left parenthesis three fourths right parenthesis superscript 6 baseline right parenthesis over left parenthesis 1 minus three fourths right parenthesis end fraction
Image with alt text: start fraction 500 times left parenthesis 1 minus left parenthesis three fourths right parenthesis superscript 6 baseline right parenthesis over left parenthesis 1 minus three fourths right parenthesis end fraction

start fraction 500 times left parenthesis 1 minus left parenthesis three fourths right parenthesis right parenthesis superscript 6 baseline over left parenthesis 1 minus three fourths right parenthesis end fraction

Answer 1

The correct expression to find the total number of grams of sugar Lana will use to make the first 6 batches of muffins is:

\[500 \times \left(1-\left(\frac{3}{4}\right)^6\right)\]

Answer 2

what does it look like as a fraction?

Answer 3

The expression \[500 \times \left(1-\left(\frac{3}{4}\right)^6\right)\] can be simplified as:

\[500 \times \left(1-\frac{729}{4096}\right)\]