MATH SOLVE

7 months ago

Q:
# In 2012, the population of a city was 6.81 million. the exponential growth rate was 1.61% per year. a) find the exponential growth function. b) estimate the population of the city in 2018. c) when will the population of the city be 10 million? d) find the doubling time.

Accepted Solution

A:

For this case we have a function of the form:

y = A * (b) ^ t

Where,

A: initial amount

b: growth rate

t: time

For each of the questions we must make use of this equation in the following way:

Part A:

y = 6.81 * (1.0161) ^ t

Part B:

y = 6.81 * (1.0161) ^ 6

y = 7.49 million

Part C:

10 = 6.81 * (1.0161) ^ t

log1.0161 ((1.0161) ^ t) = log1.0161 ((10 / 6.81))

t = log1.0161 ((10 / 6.81))

t = 24.05 years

Part D:

2 * 6.81 = 6.81 * (1.0161) ^ t

log1.0161 ((1.0161) ^ t) = log1.0161 ((2 * 6.81 / 6.81))

t = log1.0161 (2)

t = 43.40 years

y = A * (b) ^ t

Where,

A: initial amount

b: growth rate

t: time

For each of the questions we must make use of this equation in the following way:

Part A:

y = 6.81 * (1.0161) ^ t

Part B:

y = 6.81 * (1.0161) ^ 6

y = 7.49 million

Part C:

10 = 6.81 * (1.0161) ^ t

log1.0161 ((1.0161) ^ t) = log1.0161 ((10 / 6.81))

t = log1.0161 ((10 / 6.81))

t = 24.05 years

Part D:

2 * 6.81 = 6.81 * (1.0161) ^ t

log1.0161 ((1.0161) ^ t) = log1.0161 ((2 * 6.81 / 6.81))

t = log1.0161 (2)

t = 43.40 years