Question

Fresh pond has a population of 854 and is increasing by 3 people per year. Strawberry has a population of 427 and is increasing by 10% per year. Write an equation that models the growth for each town.

Answer 1

• Fresh Pond: p(t) = 854 +3t
• Strawberry: p(t) = 427·1.10^t

Explanation:

(a) The general term of an arithmetic sequence is ...

an = a1 + d(n -1)

If we let the sequence of population numbers be modeled by this, and we use t for the number of years, we want n=1 for t=0, so n = t+1 and we have ...

p(t) = 854 +3(t+1-1)

p(t) = 854 +3t

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(b) The general term of a geometric sequence is ...

an = a1·r^(n-1)

were r is the common ratio. Here, the multiplier from one year to the next is 1+10% = 1.10. Again, n=t+1, so the population equation is ...

p(t) = 427·1.10^(t+1-1)

p(t) = 427·1.10^t