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Viefleur [7K]
3 years ago
9

The population of a particular city is given by the function P(t) = 27,400(1.07)t, where t is the time in years and P(t) is the

population after t years. What is the current population, the percentage growth rate, and the population size (rounded to the nearest whole person) after 5 years? Hint: Percentage Growth Rate = r ⋅ 100 in A = A0(1 + r)t
Mathematics
1 answer:
otez555 [7]3 years ago
4 0

Answer:

27,400 is the current population

7% is the rate of increase

The new size is:

  • 38,430 is the population if t is an exponent
  • 146,590 is t is NOT an exponent in the formula you typed

Step-by-step explanation:

To find the population in a future year, use the formula:

P(t) = 27,400(1.07)t

Substitute the value t=5 to find the population in 5 years.

P(t) = 27,400(1.07)t\\P(t) = 27,400(1.07)(5)\\P(t) = 146,590


Or if the equation is supposed to have t as an exponent then look below:

P(t) = 27,400(1.07)^t

Substitute the value t=5 to find the population in 5 years.

P(t) = 27,400(1.07)^t\\P(t) = 27,400(1.07)^(5)\\P(t) = 38,430

This formula is based off the standard formula A=A_0(1+r)^t so r, the rate is 1.07=1+0.07 so r is 7%.

A_0 is the starting population which is 27,400 here.

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