Question

WILL MEDAL AND FAN.. The numbers of turtles (t) in a lake after (n) months can be defined by the recursive sequence Tn=1.04Tn-1+3 and T0=100. How many turtles are in the pond after 3 months? Round to nearest whole number

Answer 1

are you sure the formula is
\[Tn=1.04Tn-1+3\]
not
\[Tn=1.04T0-1+3\]

Answer 2

if the formula lime these it could rewrite:
\[Tn=1.04Tn-1+3\]
\[Tn=1.04Tn+2\]

Answer 3

\[T_n=1.04T_{n-1}+3?\]

Answer 4

T(n) = T(n-1) + 3
T(0) = 100

T(1) = 1.04T(0) +3 = 1.04*100 + 3 = 107

T(2) = 1.04T(1) + 3 = 1.04*107 + 3 =

Answer 5

and so on....

Answer 6

Recursion requires that you know the value of the term immediately before the term you are trying to find.

Answer 7

Find the T(2) from above, then

T(3) = 1.04*T(2) + 3 = turtles in pond after 3 months.

Answer 8

3.26 or 3 turtles in the pond? @danjs

Answer 9

No, T(2) means you use T(1) value
T(3) means you use T(2) value... see the recursion?

T(2) = 1.04*107 + 3 = 114.28 turtles
T(3) = 1.04*114.28 + 3 = 121.85

T(3) rounded to nearest whole number = about 122 turtles

Answer 10

Remember after you get an answer to check if it is reasonable. The initial number of turtles, T(0) = 100 turtles. The function increases the amount each month by, 1.04 times the previous month and add 3. So after 3 months you would expect more than 100 turtles in the pond. Three turtles is not reasonable.