Lost no idea where to start

James Smithson

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Joined
Nov 6, 2020
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27
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)


please could you guys tell me if i got the ones i answerd correct and advice me how i can answer q2

thanks :)
 

lev888

Senior Member
Joined
Jan 16, 2018
Messages
2,064
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)


please could you guys tell me if i got the ones i answerd correct and advice me how i can answer q2

thanks :)
Please post your work. Can you look at your answer for 1 and consider whether it makes sense?
 

James Smithson

New member
Joined
Nov 6, 2020
Messages
27
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 .


Answer----
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.


(i got the answer t=32.55543)
 

James Smithson

New member
Joined
Nov 6, 2020
Messages
27
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
Joined
Jan 16, 2018
Messages
2,064
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
Joined
Jan 27, 2012
Messages
7,453
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
Joined
Nov 6, 2020
Messages
27
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
 
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