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

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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step-by-step explanation: