Answer: [tex]m(t)= 10(1.21)^t[/tex]
Step-by-step explanation:
The exponential growth function in time t is given by :-
[tex]y(t)= A(b)^t[/tex]
, where a = Initial amount
b = Multiplicative factor.
Given : When it was first started, the Clinton High Cooking Club had 10 members.
The number of members increased by a factor of approximately 1.21 .
As per given , we have
A= 10
b=1.21
Then , the function that gives the number m(t) of members in the cooking club t years after it started will be :
[tex]m(t)= 10(1.21)^t[/tex] (Put values in the above function)
Growth in terms of factor shows the increment in "times". The function that gives the number m(t) of members in the cooking club t years after it started is [tex]m(t) = (1.21)^t \times 10[/tex]
Since there were initially 10 members and members are increasing with 1.21 factor each year, so after t years, we will get
[tex]m(t) = (...((10 \times (1.21 ) )\times 1.21) \times ... \times 1.21) (\rm t \: times) = 10 \times (1.21)^t\\\\m(t) = 10 + (1.21)^t[/tex]
Thus,
The function that gives the number m(t) of members in the cooking club t years after it started is [tex]m(t) = (1.21)^t \times 10[/tex]
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