Question

Can someone help on this? Please :)

Answer 1

(a) N(t) = 2(1.7)^t

(b) 17

(c) 15

Explanation:

(a) N(t) = 2(1.7)^t

There is a 2 because she starts with 2 words. The 1.7 is since her vocabulary grows by 70%. Finally, t represents the weeks. (it is an exponent)

(b) Just plug in the equation

N(4) = 2(1.7)^4

N(4) = 2(8.3521)

N(4) = 16.7042

Round, so it is 17

(c) Once again, plug in the equation

5000 = 2(1.7)^t

2500 = (1.7)^t

use a calculator for the part below

log1.7(2500) = log1.7(1.7)*t

t = log1.7(2500)

t = 14.7448

Round, so it is 15

Answer 2

N(t)=2×
`1.7^(t)`

17

15

step by step explain:

before lesson (t=0), she knows 2 words.

after a week (t=1), she knows

2×(1+70%)=3.4 words

after one more week (t=2), she knows

3.4×(1+70%)=5.78 words

one more week later (t=3), she knows

5.78×(1+70%)=9.826 words

and so on ...

from pattern shown above, we know that she knows

2×
`1.7^(t)` words after t weeks

so N(t)=2×
`1.7^(t)`

after 4 weeks (t=4), she knows 2×
`1.7^(4)`=16.7042≈17 words

for learning 5000 words, she need:

2×
`1.7^(t)`=5000

`1.7^(t)`=2500

t log(1.7)=log(2500)

t=
`(log(2500))/(log(1.7))`

=14.7448727

≈15 (round up)