Initial production (already manufactured) = 7 million doses.
Additional production = 1.4 million doses per month.
(i) After 12 months: [ \text{Total} = 7 + 1.4 \times 12 = 7 + 16.8 = 23.8 \text{ million doses}. ]
(ii) Let ( n ) be the number of months after the present.
Then
[
a_n = 7 + 1.4n
]
(in millions).
( n ) represents the number of months of additional production.
(iii) [ a_{10} = 7 + 1.4\times 10 = 7 + 14 = 21. ] After 10 months of additional production the total number of doses manufactured will be 21 million.
Answers:
(i) 23.8 million doses
(ii) ( a_n = 7 + 1.4n ) (millions), ( n ) = months of additional production
(iii) 21 million doses (after 10 months)