match each situation with its corresponding expression

This question is about exponent function. All the function in this question is following a pattern of f(x)= a(b)^t
In this function, a is the initial/starting quantity and b is the base of the exponent.

1. Answer: 7[tex] (2)^{t} [/tex]

There are 7 trout fish in the pound ----> initial value is 7, a=7
The population is double every year ------> the base is 2, b=2
f(x)= a(b)^t 
f(x)= 7(2)^t 

2. Answer: 3,000[tex] (0.93)^{t} [/tex]

Company buys a machine for $3,000 ----> initial value is 3,000, a=3,000
The value depreciate/decrease 7% a year
Since it was decreased by 7% every year, it will become: 100%-7%=93% of the original value. ------> the base is 93%, b=0.93
f(x)= a(b)^t 
f(x)= 3,000(0.93)^t 

3. Answer: 300[tex] (1.015)^{t} [/tex]

Initial population of ants is 300----> initial value is 300, a=300
The number of ants increases 1.5% per month.
Since it will increases by 1.5% every month, it will become: 100%+1.5%=101.5% of the original value. ------> the base is 101.5%, b=1.015
f(x)= a(b)^t 
f(x)= 300(1.015)^t 

4. Answer: 300[tex] (0.985)^{t} [/tex]

A research laboratory is testing new vaccine on 300 infected cells----> initial value is 300, a=300
The decay/decrease rate is 1.5% per minute
Since it will decrease by 1.5% every min, it will become: 100%-1.5%=98.5% of the original value. ------> the base is 98.5%, b=0.985
f(x)= a(b)^t 
f(x)= 300(0.985)^t