Question

2.)Suppose a population of 160 crickets doubles in size every month. The function f(x)=160*2^x

Answer 1

Answer:

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Step-by-step explanation:

1.  B. No

2. A. 2,684, 354, 560 Crickets

3. D. $9,200

4. B.  Graph

5. C.  Graph

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Answer 2

1. It is Given that

Population of 160 crickets doubles in size every month.

The function f(x)=$160\times2^x$

Population after a month= $160\times2^1$= 160 ×2= 320

Population after 2 month =  $160\times2^2$= 160 ×4= 640

(c)$160\times2^x=7,680 \\\\ 2^x= 48$→Invalid number, because number of months is a natural number.

(d) $160\times2^x=655,360 \\\\ 2^x= 4096$

$2^x=2^{14}\\\\ x=14$ months

(a)  $160\times2^x=2,684,354,560 \\\\ 2^x= 167772160$

Does not give value of x ,a natural number, as x is number representing number of months.

(2) The function which gives investment after x decades

   $f(x)=2,300\times2^x$

1 decade= 10 years

2 decade = 20 years

 $f(20)=2,300\times2^{2}$= 2300 ×4= $ 9200