Answer: y = 1000*(1.3)^x
x = number of years
y = dollar amount
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Explanation:
The growth multiplier is 1.3 because
- 1690/1300 = 1.3
- 2197/1690 = 1.3
Pick any dollar amount and divide it over its previous dollar amount to get the multiplier. The multiplier 1.3 indicates we have 30% growth because 1.3 = 1 + 0.3 = 100% + 30%
Since the multiplier is 1.3, this means b = 1.3 when referring to the exponential equation template y = a*b^x. The 'a' is the starting amount when x = 0.
To find 'a', we plug in any (x,y) ordered pair from the table.
I'll pick (x,y) = (1,1300).
So,
y = a*b^x
1300 = a*(1.3)^1
1300 = a*1.3
1300/1.3 = a
a = 1000
The starting amount is $1000
The overall equation for option 1 is y = 1000*(1.3)^x
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We can check this by plugging in x = 1
y = 1000*(1.3)^x
y = 1000*(1.3)^1
y = 1000*1.3
y = 1300
That works out.
Trying x = 2 gets us
y = 1000*(1.3)^x
y = 1000*(1.3)^2
y = 1000*1.69
y = 1690
That works also
Lastly, x = 3 leads to
y = 1000*(1.3)^x
y = 1000*(1.3)^3
y = 1000*2.197
y = 2197
All three values work out. The equation for option 1 is fully confirmed.
Side note: The equation for option 2 is not exponential. Instead, it's linear and the equation for it is y = 300x+1000
