Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match each situation to its corresponding expression. There are 7 trout fish in a pond, and the population doubles every year. Find the population after t years. arrowBoth A company buys a machine for $3,000. The value of the machine depreciates by 7% every year. Find the value of the machine after t years. arrowBoth The initial population of a colony of ants is 300. The number of ants increases at a rate of 1.5% every month. Find the population of ants after t months. arrowBoth A research laboratory is testing a new vaccine on 300 infected cells. The decay rate is 1.5% per minute. Find the number of infected cells after t minutes. arrowBoth

Step-by-step explanation:

We will use the pattern f (x) = a (b) ^t where a is the initial value, b is the base of the exponent. All these questions are about exponent function

A) Number of trout fish in the pound = 7, it means a = 7

population increases double every year. It means b=2

f (x) = a (b) ^t

f (x) = 7 (2) ^t

B) Cost of machine = $3000

The value depreciated every year = 7%

It means 100%-7% = 93% which is equal to 0.93

Therefore,

a = 3000

b = 0.93

f (x) = a (b) ^t

f (x) = 3000 (0.93) ^t

C) Initial population of a colony of ants = 300

The number of ants increase at a rate of 1.5%

It means 100%+1.5%=101.5%

101.5% = 1.015

Therefore,

a = 300

b = 1.015

f (x) = a (b) ^t

f (x) = 300 (1.015) ^t

D) A research laboratory is testing a new vaccine on 300 infected cells

The decay rate is 1.5% per minute

It means 100%-1.5% = 98.5%

98.5% = 0.985

Therefore,

a = 300

b = 0.985

f (x) = a (b) ^t

f (x) = 300 (0.985) ^t ...