Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each function to the description it models. f(x) = 150(1.6)x f(x) = 150(1.06)x f(x) = 60(1.015)x f(x) = 15(1.6)x f(x) = 60(1.15)x f(x) = 15(1.06)x A scientist initially had 15 micrograms of bacteria in a petri dish, which increased at a rate of 6% each hour. The membership price for an online retailer was initially $60 per year, but it increased at a rate of 1.5% per year. An online blog started with 150 followers, and the number of followers increased at a rate of 60% each month.

Answer 1

Answer:

Part 1) $f(x)=15(1.06)^x$

Part 2) $f(x)=60(1.015)^x$

Part 3) $f(x)=150(1.6)^x$

Step-by-step explanation:

we know that

The equation of a exponential growth is equal to

$y=a(1+r)^x$

where

a is the initial value

r is the rate of change

Part 1) we have

A scientist initially had 15 micrograms of bacteria in a petri dish, which increased at a rate of 6% each hour

Let

x ---> the number of hours

y ---> micrograms of bacteria

we have

$a=15\ micrograms\\r=6\%=6/100=0.06$

substitute

$y=15(1+0.06)^x$

$y=15(1.06)^x$

Convert to function notation

$f(x)=15(1.06)^x$

Part 2) we have

The membership price for an online retailer was initially $60 per year, but it increased at a rate of 1.5% per year

Let

x ---> the number of years

y ---> the membership price for an online retailer

we have

$a=\ 60\\r=1.5\%=1.5/100=0.015$

substitute

$y=60(1+0.015)^x$

$y=60(1.015)^x$

Convert to function notation

$f(x)=60(1.015)^x$

Part 3) we have

An online blog started with 150 followers, and the number of followers increased at a rate of 60% each month.

Let

x ---> the number of months

y ---> the number of followers

we have

$a=150\ followers\\r=60\%=60/100=0.6$

substitute

$y=150(1+0.6)^x$

$y=150(1.6)^x$

Convert to function notation

$f(x)=150(1.6)^x$