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Rewrite the logarithm as an exponential equation. (Use capital letters for variables *P* and *U*.) *P* = log_{b} *U*

Rewrite the logarithm as an exponential equation. (Use capital letters for variables *L*, *P* and *R*.) *L* = log_{b}(*P* + *R*)

Rewrite the exponential equation as a logarithm. (Use capital letters for variables *F* and *G*.) *b*^{F + 1} = *G*

Rewrite the exponential equation as a logarithm. (Use capital letters for *Q*, *F*, *S*, and *P*.) *b*^{QF} = *S* − *P*

An October 2009 article in *The Industry Standard* states that "independent Twitter data shows exponential tweet growth." GigaTweet, an independent tweet-counting service, reports that the number of tweets was 5.0 billion in October 2009. In April 2009, the number of tweets was 1.6 billion. (a) Develop the exponential growth model that fits with these data, where *t* is the number of months after April 2009 and *p* is the number of tweets in billions. (Round the coefficient of *t* to seven decimal places.)

*p*(*t*) =