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madreJ [45]
3 years ago
9

Suppose the population of a town is 2,700 and is growing 4% each year.

Mathematics
2 answers:
Papessa [141]3 years ago
6 0

Answer:

a. y=2,700(1.04)^x

b. 4,322.

Step-by-step explanation:

a. We have been given that the population of a town is 2,700 and is growing 4% each year.

We can see that population of town is increasing exponentially. Since an exponential function is in form: y=a*b^x, where,

a = Initial value.

b= For growth b is in form (1+r), where r is rate in decimal form.

y=a*(1+r)^x

Let us convert our given rate in decimal form.

4\%=\frac{4}{100}=0.04

Upon substituting a=2,700 and r=0.04 we will get,

y=2,700(1+0.04)^x

y=2,700(1.04)^x

Therefore, the equation y=2,700(1.04)^x models the population growth.

b. To find the population after 12 years we will substitute x=12 in our population growth model.

y=2,700(1.04)^12

y=2,700*1.6010322185676808

y=4,322.78699013273816\approx 4,322

Therefore, the population after 12 years will be 4,322.


8_murik_8 [283]3 years ago
3 0
Part A
Y (x)=2700 (1+0.04)^x
Y (x)=2700 (1.04)^x
where x is the number of years

Part B
Y (12)=2,700×(1.04)^(12)=4,322.78
Round your answer to get 4323
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