Question

Hannah just bought a new camera. In January she took 14 pictures. The number of pictures she took doubled each month for three months. A. how many pictures did hannah take in march? Write and solve an expression with an exponent to show how many pictures she took. B. In April, Hanna took 1/2 the number of pictures she took in March. Her brother Jack thinks she took the same number of pictures in April that she did in February. Hannah knew he was incorrect. Write and solve an expression to show why Hannah is right.

Answer 1

1) In January she took 14 pictures.

Call Ao the number of pictures she took in January => Ao = 14

2)  The number of pictures she took doubled each month for three months.

=>

month        number of pictures taken
Januray      Ao = 14
February    A1 = Ao * 2 = 14*2
March        A2 = A1 * 2 = Ao * 2 * 2 = 14 * 2^2.

how many pictures did hannah take in march? Write and solve an expression with an exponent to show how many pictures she took.

Expression: $An=Ao[2^{(x-1)}]$

where Ao is 14 and x = the number of months.

So, you can replace Ao with 14, with which the expression is $14( 2^{x-1})$

Solution: replace 3 for x, for march:

$14( 2^{3-1} )=14( 2^{2} )=14(4)=56$

B. In April, Hanna took 1/2 the number of pictures she took in March. Her brother Jack thinks she took the same number of pictures in April that she did in February. Hannah knew he was incorrect. Write and solve an expression to show why Hannah is right.

1) half the number of pictures she took is March is 14*[2^2] / 2

2) the number of pictures taken is february is14* [2^1]

Given that 14*[2^2] = 14*[2^1], Hannah is not right, her brotehr is.