transforming growth vectors

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I have two vectors. In v1 growth begins quickly and then slows down. In v2 growth begins slowly but then quickly accelerates

v1 <- c(1,25,39,49,59,58,66,69,76,78,82,86,87,87,88,86)
v2 <- c(1,2,1,3,2,2,4,3,5,14,29,45,68,90,140,200)

I'm trying to make both vectors look more linear

log does a decent job on v2

plot(log(v2))

but how should I transform v1? exp does a terrible job

plot(exp(v1))

Is there a generic R function I can use for growth rates such as v1?

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