Question

Determine the models that could represent a compound interest account that is growing exponentially.

Select all the correct answers,

A(t) = 2,675(1.003)120

A(t) = 4,170(1.04)

A(t) = 3,500(0.997)4t

A(t) = 5,750(1.0024)20

A(t) = 1,500(0.998)127

A(t) = 2,950(0.999)

Answer 1

Answer:
`A(t) = 2,675(1.003)^(120)`

`A(t) = 4,170(1.04)`

`A(t) = 5,750(1.0024)^(20)`

Explanation:

The exponential growth equation is given by :-

`y=Ab^x` , where A = initial value , x= time period , b= growth factor.

The growth factor should be greater than 1.

From all the given options , the equations that are exponential :

`A(t) = 2,675(1.003)^(120)` , here b= 1.003

`A(t) = 4,170(1.04)` , here b= 1.04

`A(t) = 3,500(0.997)^(4t)` , here b= 0.997

`A(t) = 5,750(1.0024)^(20)` , here b= 1.0024

`A(t) = 1,500(0.998)^(127)` , here b= 0.998

`A(t) = 2,950(0.999)` , here b= 0.999

From the above exponential equations , only first , second and fourth equation has b>1.

So , the models that could represent a compound interest account that is growing exponentially. are :

`A(t) = 2,675(1.003)^(120)`

`A(t) = 4,170(1.04)`

`A(t) = 5,750(1.0024)^(20)`