The median age for a first marriage in the United States for men was 28.1 in 2009 and 28.2 in 2010. Use an exponential model to predict the median age for men in 2019, where x is the number of years since 2009.

Question

eviant · Answer

@Vocaloid

Vocaloid · Answer

same logic as last time, you are given

(0,28.1) and (1,28.2) 
y = ab^x, where a is the initial value 28.1 and b is the growth rate, x is the years since 2009
plugging this into y = ab^x gives us

(28.2) = (28.1)b^(1), solve for b again, then re-write y = ab^x

eviant · Answer

@Vocaloid 27.1?

Vocaloid · Answer

if (28.2) = (28.1)b^1 what does b equal? you just have to divide both sides by 28.1

Vocaloid · Answer

(28.2) = (28.1)b^1 
b = 28.2/28.1

eviant · Answer

27.0
 	
27.1
 	
29.3
 	
29.2

eviant · Answer

^^^those are the options

Vocaloid · Answer

notice that the average age of marriage is increasing so it can't be 27.0 or 27.1

re-writing our exponential function gives us

y = 28.1(28.2/28.1)^x

10 years passed between 2009 and 2019, so x = 10, plug in and solve for y

eviant · Answer

29.2

Vocaloid · Answer

yeah that's what i got too 
i'm not 100% sure but that's my best attempt