Question

Exponential Growth/Decay Plz help!!!

Answer 1

Answer:

a) 82.

b) So a growth factor of 0.025

c) 2.5%.

d) f(5) = 93, which means that the population of the island on January 1st 2026 is of 93.

Step-by-step explanation:

Exponential equation of population growth:

The exponential equation for population growth has the following format:

$f(x) = x(0)(1+r)^x$

In which x(0) is the initial value and r is the growth factor, as a decimal.

In this question:

In x years after 2021:

$f(x) = 82(1.025)^x$

a)

This is f(0). So

$f(0) = 82(1.025)^0 = 82$

So 82.

b)

We have to find r. So

$1 + r = 1.025$

$r = 1.025 - 1 = 0.025$

So a growth factor of 0.025.

c)

Growth factor multiplied by 100%.

So 0.025*100% = 2.5%.

d)

f(5) = population in 5 years after January 1st 2021, that is, January 1st 2026.

$f(5) = 82(1.025)^5 = 93$

f(5) = 93, which means that the population of the island on January 1st 2026 is of 93.