Question

Frogs – A species of frog’s population grows 24% every year. Suppose 100 frogs are released into a pond. (For some answers, you should round to whole frogs.)

Construct an exponential model for this population.

How many frogs will there be in 5 years?

How many frogs will there be in 10 years?

About when will there be 1000 frogs? (Round to a whole year.)

Answer 1

293; 869; 11 years

Explanation:

N: no. of frogs

t: no. of years

N = 100(1.24^t)

N = 100(1.24⁵)

= 293

N = 100(1.24¹⁰)

= 859

1000 = 100(1.24^t)

10 = 1.24^t

lg10 = t×lg1.24

t = 1/lg1.24

t = 10.7 = 11 years

Answer 2

Explanation:

We would apply the formula for exponential growth which is expressed as

A = P(1 + r)^ t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 100

r = 24% = 24/100 = 0.24,

The exponential model for this population becomes

A = 100(1 + 0.24)^t

A = 100(1.24)^t

1) When t = 5 years,

A = 100(1.24)^5

A = 293

2) When t = 10 years,

A = 100(1.24)^10

A = 859

3) When A =1000

1000 = 100(1.24)^t

1000/100 = (1.24)^t

10 = (1.24)^t

Taking log of both sides to base 10, it becomes

Log 10 = log 1.24^t

1 = t log 1.24

1 = 0.093t

t = 1/0.093

t = 11 years to the nearest whole year.