please help me finish the problem and include your steps please ( I already solv

Question

please help me finish the problem and include your steps please ( I already solved the first part)

The cities of Abnarca and Bonipto have populations that are growing exponentially. In 1980, Abnarca had a population of 21,000 people. In 1990, its population was 24,000. Bonipto had a population of 36,000 in 1980. The population of Bonipto doubles every 55 years. (Round your answers to the nearest whole number.)

(a) How long does it take the population of Abnarca to double?

52 yr

(b) How long will it take for Abnarca's population to equal that of Bonipto?

Explanation / Answer

Abnarca :
In 1980, Abnarca had a population of 21,000 people. In 1990, its population was 24,000.

So, we have
(0 , 21000)
(10 , 24000)

Using y = a*b^(t), we get :
21000 = a*b^0
a = 21000

And thus
y = 21000*(b)^t

Using (10 , 24000) :
24000 = 21000*b^10
b = 1.01344269

And thus,
y = a*b^t

y = 21000 *(1.01344269)^t ---> Abnarca

Doubling time :
42000 = 21000*(1.01344269)^t

2 = 1.01344269^t

t = ln(2)/ln(1.01344269)

t = 51.9089329203436316 yrs to double ---> FIRST ANSWER

----------------------------------------------------------

Bonipto had a population of 36,000 in 1980. The population of Bonipto doubles every 55 years

So, we have
y = 36000*(b)^t

Now, it doubles every 55 yrs :
So, we have

72000 = 36000*b^(55)

2 = b^55

b = 2^(1/55)

b = 1.012682

And thus
y = 36000*(b)^t
becomes

y = 36000*(1.012682)^t ---> For Bonipto

Now, when will their populatiokns be equal?
Lets find out

21000 *(1.01344269)^t = 36000*(1.012682)^t

Solving, we get :
36000/21000 = (1.01344269)^t / (1.012682)^t

1.7142857142857143 = 1.0007511637414312^t

t = ln(1.7142857142857143)/ln( 1.000751163741431)

t = 718 yrs approx ----> ANS

So, it will take 718 yrs for the populations to be equal

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