If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

# Exponential vs. linear models: verbal

CCSS.Math:

## Video transcript

a newborn calf weighs 40 kilograms each week its weight increases by 5% let W be the weight in kilograms of the calf after t weeks is w a linear function or an exponential function so this if W or a linear function that means that every week that goes by the weight would increase by the same amount so let's say that every week that went by the weight increases are really they're talking about mass here the mass increased by five kilograms then we'd be dealing with a linear function but they're not saying that the weight increases by five kilograms they're saying by five percent so after one week it'll be 1.0 five times 40 kilograms after another week it'll be 1.0 five times that'll be five percent more after the next week it'll be 1.0 five times that so really what we really think about this function it's going to be 40 kilograms times 1.05 to the T power we're compounding by five percent every time we're increasing by a factor of one point zero five another way of thinking by by a factor of 100 five percent every week so because we have that that growth by a factor not just by a constant number that tells us that tells us that this is going to be an exponential function so let's see which of these choices describe that this function is linear now we'd have to even read that this function is linear nope this function is exponential because W increases by a factor of five each time T increases by one no that's not right we're increasing by five percent increasing by 5% means you're 1.0 five times as big as you were before increasing so it's really this function is exponential because W increases by a factor of 1.05 each time T increases by one that right over there is the right answer let's try one more of these determine whether the quantity described is changing in a linear fashion or an exponential fashion Fidel has a rare coin worth \$550 each year the coins value increases by 10% well this is just like the last example we saw we're increasing every year that goes by as we increase by a factor of 1.1 if we grow by 10% that's increasing by a factor of 110 percent or 1 point 1 so this is definitely exponential if it was increasing \$10 per year then it would be linear but here we're increasing by a percentage your uncle bought a car for 130,000 Mexican pesos each year the value of the car decreases by 10,000 pesos so here we're not we're not multiplying by a factor we're decreasing by a fixed amount you're one year goes by we're at 120 thousand two years goes by 110 thousand so this is definitely a linear this is can be described as by a linear model the number of wild hogs in Arkansas increases by a factor of three every five years so a factor of three every five years they're not saying it increases by three hogs every five years we're mean we're multiplying by three every five years so this is definitely this one right over here is going to be exponential and then finally you work as a waiter at a restaurant you were in \$50 in tips every day you were well this is super this is you know this should jump out as very linear every day you work another \$50 work one day \$50 two days \$100 so forth and so on they're not saying that you're in 50 times as much as the day before they're not saying that you aren't 50 percent more they're saying that you're increasing by a fixed quantity so this is going to be a linear model