Question

(a)The population of a city is increasing exponentially at a rate of 2% each year. The population now is 256 000. Calculate the population after 30 years. Give your answer correct to the nearest thousand.




(b) A bacteria population increases exponentially at a rate of r% each day. After 32 days, the population has increased by 309%. Find the value of r.

Answer 1

Sorry.. Good Luck with the answer tho!...

Answer 2

(a)The population of the city after 30 years will be 463708.566 as per exponential growth.

(b) The value of the exponential 'r' is 4.5%.

What is the exponential growth of a system?

"Exponential growth is a process that increases quantity over time."

Here, f(x) = a(1 + r)ˣ

f(x) = exponential growth function

a = initial amount

r = growth rate

x = number of time intervals

(a)The population of the city is (A) = 256,000.

The rate of increase of population per year is (r) = 2% = 0.02.

Time period (n) = 30 years.

Therefore, the population after 30 years

= A(1 + r)ⁿ

= 256000(1 + 0.02)³⁰

= 463708.566

(b) Let, the total bacteria is x.

The rate of increase of bacteria per day is = r%

Time period (n) = 32 days.

Total increased in bacteria in 32 days = 309%.

After 32 days, the total number of bacteria is

= x + (x × 309/100)]

= x + 3.09x

= 4.09x

Therefore,

4.09x = $x(1 + r)^{t}$

⇒ $(1 + r)^{32}$ = 4.09

⇒ (1 + r ) = 1.045

⇒ r = 0.045

⇒ r = 4.5%

Learn more about exponential growth here: https://brainly.com/question/18118767

#SPJ3