# Lost no idea where to start

#### James Smithson

##### New member
A childs vocabulary up to 36 months can be modeld by a exponetial model with equation .
v=0.27x(126)^t (v is vocab and t is age in months)

my 3 questions are

1. calculate the size of vocab for a child age 18 months and a child aged 30 months . 18 months v = 17.299501 30 months v = 2.77000222

(so i think i got this right)

2. wright down the scale factor and use it to find the percentage increase in vocab each month. (i have no idea how to attempot this the only scale factoring i have done is in shapes )

3 find the age of a child when they know 500 words. (i got the answer t=32.55543)

thanks

#### lev888

##### Senior Member
A childs vocabulary up to 36 months can be modeld by a exponetial model with equation .
v=0.27x(126)^t (v is vocab and t is age in months)

my 3 questions are

1. calculate the size of vocab for a child age 18 months and a child aged 30 months . 18 months v = 17.299501 30 months v = 2.77000222

(so i think i got this right)

2. wright down the scale factor and use it to find the percentage increase in vocab each month. (i have no idea how to attempot this the only scale factoring i have done is in shapes )

3 find the age of a child when they know 500 words. (i got the answer t=32.55543)

thanks

#### James Smithson

##### New member
Sorry it was a bit jumbled is this better ?

1. calculate the size of vocab for a child age 18 months and a child aged 30 months .

18 months v = 17.299501 (rounded to 17)
30 months v = 277.000222 (rounded to 277)
realise I said 2.77 on the original post oops )

(so i think i got this right)

2. wright down the scale factor and use it to find the percentage increase in vocab each month.

(i have no idea how to attempot this the only scale factoring i have done is in shapes )

3 find the age of a child when they know 500 words.

#### James Smithson

##### New member
1.
v=0.27*(1.26)^t

v is vocabulary t is age in months so when a child is 18 months.
v = 0.27 x (1.26)^18
Simplified that is
v=17.299,,,
v=17.3( to 1 d.p)

so a childs vocabulary is aproximatly 17 words at 18 months old.

And when 30 months

v= 0.27 * (1.26)^30
v=277.0002...
v=277.0 (to 1 d.p)

so a childs vocabulary is aproximatly 277 words aged 30 monthys acording to the model

2???????????????/

3.
v= 0.27(1.26)^t
500 = 0.27(1.26)^t
divide both sides by 0.27
1851.851852 =1.26^t
flip sides then
take log of both sides
t=32.55...
t= 32.6 (to 1 d.p)

#### lev888

##### Senior Member
wright down the scale factor and use it to find the percentage increase in vocab each month.
Scale factor = vocabulary at n divided by vocabulary at n-1.

#### HallsofIvy

##### Elite Member
2. wright down the scale factor and use it to find the percentage increase in vocab each month.
Of course you mean "write". What "definition" of "scale factor" were you given?

Not knowing that, but jumping the second part of this question, in month t, the child's vocabulary is $$\displaystyle V(t)= 0.27(1.26)^t$$. The next month it is $$\displaystyle 0.27*(1.26)^{t+1}= 0.27*(1.26)^t(1.26)= 1.26V(t)$$. The child's vocabulary has increased by a factor of 1.26 (I'll bet that's the "scale factor"!) which is a 26% increase.

#### James Smithson

##### New member
Of course you mean "write". What "definition" of "scale factor" were you given?

Not knowing that, but jumping the second part of this question, in month t, the child's vocabulary is $$\displaystyle V(t)= 0.27(1.26)^t$$. The next month it is $$\displaystyle 0.27*(1.26)^{t+1}= 0.27*(1.26)^t(1.26)= 1.26V(t)$$. The child's vocabulary has increased by a factor of 1.26 (I'll bet that's the "scale factor"!) which is a 26% increase.
We were not given a definition and that's why I'm struggling they leave it to our interpretation